arXiv subjects

Jiahong Wu

Publications and source records attributed to Jiahong Wu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Nonlinear stability of a background magnetic field for the 3D compressible MHD equations with anisotropic dissipation

We study the nonlinear stability of an equilibrium with a background magnetic field for the three-dimensional compressible magnetohydrodynamic (MHD) equations in the whole space $\mathbb{R}^3$, in the strongly anisotropic regime where the velocity is dissipated only in the horizontal directions and the magnetic field is diffused in a single direction. We prove that for initial data sufficiently close to the equilibrium in a Sobolev space, the system admits a unique global-in-time solution that remains close to the equilibrium and enjoys quantitative dissipation estimates. The proof overcomes the severe lack of dissipation through two mechanisms: the background magnetic field is shown to generate enhanced dissipation for the magnetic field and the density, while a nonlinear cancellation mechanism is devised to resolve the loss of vertical derivatives caused by the compressible coupling.

math.AP↗

arXiv2026

Global stability and anisotropic large-time behavior of the three-dimensional compressible Navier--Stokes equations with eddy diffusion

We study the Cauchy problem for the three-dimensional compressible Navier--Stokes equations with eddy diffusion, an anisotropic dissipative mechanism that arises naturally in geophysical fluid dynamics (cf.~\cite{Jabin-Bresch-2018,Temam-Ziane-2004}). In contrast to the classical compressible Navier--Stokes system, the momentum equation here carries no full vertical Laplacian: the velocity is diffused only in the horizontal directions, and the sole vertical regularization it receives is the partial one transmitted through the compressible mode $\operatorname{div}\mathbf{u}$. This degeneracy invalidates the standard parabolic energy framework as well as the classical high--low frequency Green-function bounds. We prove that the constant non-vacuum equilibrium $(\barρ,0)$ is globally nonlinearly stable against small Sobolev perturbations: global classical solutions exist in $H^{N}(\mathbb{R}^{3})$ for every $N\ge 3$, and the density and velocity relax to equilibrium with explicit, genuinely anisotropic decay rates. The mechanism behind the result is a hidden dissipation produced by the pressure--divergence coupling between $\nablaρ$ and $\operatorname{div}\mathbf{u}$, which compensates for the missing vertical smoothing of the density and the compressible part of the velocity; the solenoidal part of the velocity, by contrast, is governed by a purely horizontal heat flow and therefore decays only at the two-dimensional rate. The analysis rests on a refined anisotropic spectral decomposition of the Green matrix, a div--curl treatment of the velocity, and time-weighted nonlinear energy estimates tailored to the degenerate dissipation. To the best of our knowledge, this is the first global stability and large-time behavior result for the three-dimensional compressible Navier--Stokes equations with eddy diffusion in the whole space.

math.AP↗

arXiv2026

Stability of vertically charged steady magnetic field in 3D incompressible magneto-micropolar fluids without magnetic and angular viscosity in a strip domain

This paper intends to understand the regularity and stability problem on the 3D incompressible magneto-micropolar equations with zero magnetic and angular viscosities in a strip domain. The magneto-micropolar system models the electrically conducting micropolar fluid in the presence of a magnetic field. The lack of magnetic diffusion and angular dissipation makes it impossible to prove even small data global well-posedness result, let alone general large data global regularity. This paper presents a steady-state setup around which any perturbations can be shown to be globally regular and stable. More precisely, any small perturbation near a steady magnetic field perpendicular to the horizontal boundary leads to a unique global classical solution. In addition, the solution is shown to converge to the steady state at an almost exponential rate as time goes to infinity. These appear to be the very first rigorous global results on the magneto-micropolar equations concerned here.

math.AP↗

arXiv2026

A consistent-splitting generalized scalar auxiliary variable scheme for the perturbed Boussinesq system

We propose and analyze a second-order consistent-splitting scheme, based on the generalized scalar auxiliary variable (GSAV) approach, for the two-dimensional perturbed Boussinesq system. The system is obtained by subtracting a stable, linearly stratified hydrostatic equilibrium from the standard Boussinesq system. The time discretization extends the consistent-splitting generalized BDF2 framework of Huang and Shen [17] for the Navier-Stokes equations, treating the nonlinear convection and advection together with the linear buoyancy and stratification couplings explicitly, so that each time step reduces to a small number of decoupled linear systems. We prove an unconditional weak stability theorem for the GSAV scheme and derive optimal second-order error estimates for the velocity, pressure, and temperature. A careful tracing reveals that the error constant depends on the inverse viscosity and inverse thermal diffusivity through a quadruply-nested exponential, so the scheme is not robust as either tends to zero. Numerical experiments confirm the second-order convergence and reproduce the expected internal-wave dynamics and exponential relaxation toward hydrostatic balance in a long-time stratified-flow simulation.

math.NA↗

arXiv2026

OmniDance: Multimodal Driven Dance Video Generation with Large-scale Internet Data

Music-driven dance video generation aims to synthesize expressive human motion that is temporally aligned with music while maintaining high visual fidelity. Despite recent progress, existing methods still face two key limitations: the lack of large-scale, high-quality dance video datasets, and the absence of principled frameworks for integrating music as a complementary conditioning signal into Video Generation Foundation Models. To address these limitations, we introduce CIPE-Dance, a large-scale Internet-sourced dance video dataset with choreography-informed text annotations, constructed via a progressive expert pipeline. To the best of our knowledge, CIPE-Dance is the largest dataset for dance video generation to date, comprising 300k high-quality clips over 400 hours and covering diverse dancers, environments, and dance genres. We further propose OmniDance, a framework-level recipe for integrating music into a TI2V foundation model without sacrificing its original controllability or visual fidelity. Motivated by the complementary roles of text as low-frequency semantics and music as high-frequency temporal dynamics, OmniDance co-designs a depth-aware specialization architecture, an anchored easy-to-hard curriculum learning strategy, and a modality-specialized time-dependent CFG strategy, enabling unified TI2V, MI2V, and MTI2V generation. Extensive experiments on CIPE-Dance demonstrate that OmniDance achieves state-of-the-art performance across all three tasks and exhibits robust multimodal integration capability. Project is available at https://github.com/AMAP-ML/OmniDance.

cs.CV↗

arXiv2026

Stabilizing effect of a background magnetic field on the 2D damped wave-type MHD equations

The stabilizing effect of a background magnetic field on electrically conducting fluids has been rigorously established for the standard MHD equations. This paper extends this theory to the more physically accurate damped wave-type MHD equations, where the induction equation is hyperbolic-parabolic and the velocity field has only vertical damping with no dissipation. These two features make the stability analysis harder than in the standard MHD setting. To overcome these difficulties, we design an energy functional exploiting the anisotropic structure, and discover a remarkable cancellation between the two most dangerous nonlinear terms by exploiting the full algebraic structure of the coupled system. As a consequence, we prove that any small perturbation near the background magnetic field is globally stable and establish optimal decay rates consistent with the 2D heat equation. To the best of our knowledge, this is the first rigorous stability result for the damped wave-type MHD equations near a background magnetic field.

math.AP↗

arXiv2026

Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations

This paper investigates the role of viscosity in the error upper bounds of a consistent splitting scheme for the Navier-Stokes equations proposed by Huang and Shen [5]. In their original analysis the viscosity is fixed to unity. By following and extending their proof methodology while keeping the viscosity symbolic, we obtain an H1 velocity error bound that contains negative powers of viscosity, indicating that the scheme is not robust as viscosity tends zero. To establish this bound we refine a theorem in [8] on the constant in the Stokes pressure estimate, which is crucial to the error analysis. A targeted numerical experiment based on a perturbation of the Kovasznay flow corroborates this analytical prediction: the scheme of [5] blows up at high Reynolds number, and a comparison with a fully implicit Newton solver and with the time-dependent Stokes counterpart of the same scheme localizes the failure to the explicit treatment of the convection term.

math.NA↗

arXiv2026

DreamX-World 1.0: A General-Purpose Interactive World Model

DreamX-World 1.0 is a general-purpose interactive text/image-to-video world model for controllable long-horizon generation. It supports camera navigation, revisits to previously observed regions, and promptable events across photorealistic, game-style, and stylized domains. Our data engine combines camera-accurate Unreal Engine rendering, action-rich gameplay recordings, and real-world videos with recovered camera geometry. For camera control, we introduce E-PRoPE, a lightweight variant of projective positional encoding that retains PRoPE's projective camera geometry while applying camera-aware attention to spatially reduced tokens. We convert a bidirectional video generator into a few-step autoregressive world model using causal forcing, DMD-style distillation, and long-rollout training. Training on self-generated long-horizon contexts exposes the model to its own generated history and reduces the style and color drift that accumulates across autoregressive chunks. Memory-Conditioned Scene Persistence retrieves earlier views through camera-geometry-based retrieval, while residual recycling makes the conditioning path less sensitive to imperfect memory latents. Event Instruction Tuning adds composable event control, and reinforcement learning alignment recovers camera control and visual quality after distillation. With mixed-precision DiT execution, residual reuse, 75\%-pruned VAE decoding, and asynchronous pipeline parallelism, DreamX-World 1.0 reaches up to 16\,FPS on eight RTX\,5090 GPUs. On our 5-second basic evaluation, DreamX-World 1.0 achieves a camera-control score of 73.75 and an overall score of 84.76, outperforming HY-WorldPlay 1.5 and LingBot-World in overall score, which achieve 80.79 and 80.45, respectively.

cs.CV↗

arXiv2026

Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation

This paper studies the global regularity problem for the two-dimensional incompressible Boussinesq equations with fractional dissipation given by $(-Δ)^{\frac\alpha2}u$ and $(-Δ)^{\frac\beta2} θ$. Attention is focused on the subcritical regime where $α+ β>1$. The case $α>\frac23$ was recently settled in a joint work of the authors [Math. Ann., \textbf{391} (2025), 5965-6012], which established global regularity under this condition. This paper addresses the remaining case $α\leq \frac23$. We obtain the sharpest regularity result by minimizing assumptions on $α$ and $β$. We derive nonlinear lower bounds for the fractional Laplacian operator and implement an iterative procedure.

math.AP↗

arXiv2026

Global uniform regularity and vanishing vertical viscosity limit for the compressible Navier--Stokes equations in the half-space

In geophysical flows such as large-scale ocean dynamics, the vertical viscosity is often much smaller than the horizontal viscosity. This anisotropy makes it natural to ask whether solutions of the full anisotropic compressible Navier--Stokes equations converge, as the vertical viscosity coefficient $\varepsilon \to 0$, to solutions of a horizontally dissipative limit system, and whether this limit can be justified globally in time. Prior work has answered this question locally in time or in the incompressible setting. We resolve this problem for the three-dimensional compressible Navier--Stokes equations in the upper half-space with the Navier slip boundary condition. This paper establishes two main results for small perturbations of a constant equilibrium state. First, we prove the existence of a unique global-in-time solution whose conormal Sobolev norm remains uniformly bounded for all $t \ge 0$ and all $\varepsilon \in (0,1)$. Second, we justify the global vanishing vertical viscosity limit. More precisely, we show that the solutions converge to a global solution of the horizontally dissipative compressible Navier--Stokes system. This provides the first rigorous justification of the anisotropic viscosity limit for compressible flows on an infinite time interval.

math.AP↗

arXiv2026

DocOS: Towards Proactive Document-Guided Actions in GUI Agents

While Graphical User Interface (GUI) agents have shown promising performance in automated device interaction, they primarily depend on static parametric knowledge from pre-training or instruction tuning. This reliance fundamentally limits their ability to handle long-tailed tasks that require explicit procedural knowledge absent from model parameters, often forcing agents to resort to inefficient and brittle trial-and-error exploration. To mitigate this limitation, we introduce \textbf{Proactive Document-Guided Action} for GUI agents in dynamic, open-web environments, a novel paradigm that mirrors human problem-solving by enabling agents to autonomously search for relevant documentation to resolve long-tailed tasks. To evaluate agents' capability in this paradigm, we propose \textbf{DocOS}, a benchmark designed to assess document-guided problem solving in fully interactive environments. DocOS requires agents to autonomously navigate a web browser, locate relevant online documentation, comprehend procedural instructions, and faithfully ground them into executable GUI actions. Extensive experiments reveal that progress is strictly constrained by dual bottlenecks: agents struggle to reliably locate relevant information during proactive search and frequently fail to faithfully ground retrieved instructions into precise actions, pointing toward document-guided interaction as a crucial pathway for enabling self-evolving GUI agents in dynamic environments.

cs.AI↗

arXiv2026

Embedding-perturbed Exploration Preference Optimization for Flow Models

Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay of intra-group variance. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into premature stagnation or reward hacking. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in training instability or diminishing returns. To overcome these challenges, we propose $\textbf{Embedding-perturbed Exploration Preference Optimization (}E^2\textbf{PO)}$, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.

cs.CV↗

arXiv2026

Sharp decay characterization for the incompressible Oldroyd-B model in critical $L^p$ spaces

This paper establishes a sharp characterization of temporal decay rates for the incompressible Oldroyd-B model in a critical $L^p$ framework, covering the physically relevant and mathematically delicate case where both the fluid viscosity and the stress tensor damping are absent. We prove that an $L^2$-type condition on the low-frequencies part of the initial data $(u_0, τ_0)$ is almost both necessary and sufficient for obtaining optimal upper and lower bounds on the temporal decay of solutions in critical Besov spaces. A key contribution is a new decomposition of the stress tensor into its incompressible and compressible parts, combined with the introduction of an effective tensor to handle the loss of regularity in the high-frequencies velocity field. This is the first result to reveal such precise two-sided asymptotics for the incompressible Oldroyd-B model without viscosity or damping.

math.AP↗

arXiv2026

Global uniform regularity for the 3D compressible MHD equations near a background magnetic field

This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical applications, we consider an anisotropic compressible MHD system with weak dissipation in the $x_2$ and $x_3$ directions and small vertical magnetic diffusion. By exploiting the stabilizing effect induced by the background magnetic field and constructing a hierarchy of four energy functionals, we establish global-in-time uniform bounds that are independent of the viscosity in the $x_2$ and $x_3$ directions and the vertical resistivity. A key innovation in our analysis is the development of a two-tier energy method, which couples the boundedness of vertical derivatives with the decay of horizontal derivatives. The analysis of time scale, together with global regularity estimates and sharp decay rates, enable us to rigorously justify the vanishing dissipation limit and derive explicit long-time convergence rates to the compressible MHD system with vanishing dissipation in the $x_2$ and $x_3$ directions and no vertical magnetic diffusion. In the absence of magnetic field and background magnetic field, the global-in-time well-posedness and vanishing viscosity limit for the 3D compressible Navier-Stokes equations with only one direction dissipation remains a challenging open problem. This work reveals the mechanism by which the magnetic field enhances dissipation and stabilizes the fluid dynamics in the global well-posedness and vanishing viscosity limit.

math.AP↗

arXiv2026

MACE-Dance: Motion-Appearance Cascaded Experts for Music-Driven Dance Video Generation

With the rise of online dance-video platforms and rapid advances in AI-generated content (AIGC), music-driven dance generation has emerged as a compelling research direction. Despite substantial progress in related domains such as music-driven 3D dance generation, pose-driven image animation, and audio-driven talking-head synthesis, existing methods cannot be directly adapted to this task. Moreover, the limited studies in this area still struggle to jointly achieve high-quality visual appearance and realistic human motion. Accordingly, we present MACE-Dance, a music-driven dance video generation framework with cascaded Mixture-of-Experts (MoE). The Motion Expert performs music-to-3D motion generation while enforcing kinematic plausibility and artistic expressiveness, whereas the Appearance Expert carries out motion- and reference-conditioned video synthesis, preserving visual identity with spatiotemporal coherence. Specifically, the Motion Expert adopts a diffusion model with a BiMamba-Transformer hybrid architecture and a Guidance-Free Training (GFT) strategy, achieving state-of-the-art (SOTA) performance in 3D dance generation. The Appearance Expert employs a decoupled kinematic-aesthetic fine-tuning strategy, achieving state-of-the-art (SOTA) performance in pose-driven image animation. To better benchmark this task, we curate a large-scale and diverse dataset and design a motion-appearance evaluation protocol. Based on this protocol, MACE-Dance also achieves state-of-the-art performance. Code is available at https://github.com/AMAP-ML/MACE-Dance.

cs.CV↗

arXiv2026

Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation on $\mathbb{R}^2$

The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the inviscid Euler. Navier-Stokes solutions in $\mathbb R^2$ decay algebraically in time while Euler solutions can grow rather rapidly in time. This paper solves the fundamental stability and large-time behavior problem on the anisotropic Navier-Stokes with fractional dissipation $Λ_1^{2s}$ for all $0\leq s<1$. The case $s=1$ corresponds to the standard one directional dissipation $\partial_1^2$. Different techniques are developed to treat different ranges of fractional exponents: $0\leq s\leq \frac34$, $\frac34<s<\frac{11}{12}$, and $\frac{11}{12} \leq s <1$. The final range is the most difficult case, for which we introduce the spatial polynomial $A_2$ weights and exploit the boundedness of Riesz transforms on weighted $L^2$-spaces.

math.AP↗

arXiv2026

Extending One-Step Image Generation from Class Labels to Text via Discriminative Text Representation

Few-step generation has been a long-standing goal, with recent one-step generation methods exemplified by MeanFlow achieving remarkable results. Existing research on MeanFlow primarily focuses on class-to-image generation. However, an intuitive yet unexplored direction is to extend the condition from fixed class labels to flexible text inputs, enabling richer content creation. Compared to the limited class labels, text conditions pose greater challenges to the model's understanding capability, necessitating the effective integration of powerful text encoders into the MeanFlow framework. Surprisingly, although incorporating text conditions appears straightforward, we find that integrating powerful LLM-based text encoders using conventional training strategies results in unsatisfactory performance. To uncover the underlying cause, we conduct detailed analyses and reveal that, due to the extremely limited number of refinement steps in the MeanFlow generation, such as only one step, the text feature representations are required to possess sufficiently high discriminability. This also explains why discrete and easily distinguishable class features perform well within the MeanFlow framework. Guided by these insights, we leverage a powerful LLM-based text encoder validated to possess the required semantic properties and adapt the MeanFlow generation process to this framework, resulting in efficient text-conditioned synthesis for the first time. Furthermore, we validate our approach on the widely used diffusion model, demonstrating significant generation performance improvements. We hope this work provides a general and practical reference for future research on text-conditioned MeanFlow generation. The code is available at https://github.com/AMAP-ML/EMF.

cs.CV↗

arXiv2026

MAR-GRPO: Stabilized GRPO for AR-diffusion Hybrid Image Generation

Reinforcement learning (RL) has been successfully applied to autoregressive (AR) and diffusion models. However, extending RL to hybrid AR-diffusion frameworks remains challenging due to interleaved inference and noisy log-probability estimation. In this work, we study masked autoregressive models (MAR) and show that the diffusion head plays a critical role in training dynamics, often introducing noisy gradients that lead to instability and early performance saturation. To address this issue, we propose a stabilized RL framework for MAR. We introduce multi-trajectory expectation (MTE), which estimates the optimization direction by averaging over multiple diffusion trajectories, thereby reducing diffusion-induced gradient noise. To avoid over-smoothing, we further estimate token-wise uncertainty from multiple trajectories and apply multi-trajectory optimization only to the top-k% uncertain tokens. In addition, we introduce a consistency-aware token selection strategy that filters out AR tokens that are less aligned with the final generated content. Extensive experiments across multiple benchmarks demonstrate that our method consistently improves visual quality, training stability, and spatial structure understanding over baseline GRPO and pre-RL models. Code is available at: https://github.com/AMAP-ML/mar-grpo.

cs.CV↗