arXiv subjects

Nangao Zhang

Publications and source records attributed to Nangao Zhang.

5 recordsLinked to original sources

arXiv2026

Stability threshold of the Couette flow in 2D Navier-Stokes Boussinesq equations on $\mathbb{T} \times [-1, 1]$ and $\mathbb{R} \times [-1, 1]$

In this paper, we study the transition threshold problem for the 2D Navier-Stokes Boussinesq equations around the Couette flow with a constant background temperature in two domains: $\mathbb{T} \times [-1, 1]$ and $\mathbb{R} \times [-1, 1]$. It was proved that if the sizes of initial perturbations of the vorticity and the temperature in Sobolev spaces are $ν^{\fr13}$ and $ν^{\fr56}$, respectively, then this system admits a globally stable solution. Besides, we derive the enhanced dissipation estimate for the vorticity and temperature, as well as the inviscid damping estimate for the velocity. The coupling in the equations poses some difficulties to the analysis. We overcome these challenges and establish the results via the quasi-linear method and energy estimates.

math.AP↗

arXiv2026

Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations

We study the transition threshold problem for the 2D Navier--Stokes Boussinesq equations around the Poiseuille flow on three domains: $\mathbb{T} \times \mathbb{R}$, $\mathbb{T} \times [0, \infty)$, and $\mathbb{T} \times [-1, 1]$. More precisely, we prove that if the initial perturbations of the vorticity and the temperature are assumed size $O(\min\{ν^{\fr34},μ^{\fr34},ν^{-\fr14}μ\})$ and $O(\min\{ν^{\fr94},μ^{\fr94}\})$ in an anisotropic Sobolev space respectively, then for the solution to this system, its size remains so for all time, and the nonlinear enhanced dissipation persists with a rate proportional to $O(\min\{ν^{\fr12},μ^{\fr12}\})$.

math.AP↗

arXiv2025

Boundary effect on asymptotic behaviour of solution to the hyperbolic-parabolic chemotaxis system

This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular networks observed invitro experiment. Under two diffrent boundary conditions,we first establish the existence and uniqueness of the solution of the asymptotic state equation (the so-called nonlinear diffusion wave),and then prove that the solution of the original equation is nonlinearly asymptotically stable. Additionally,we obtain the convergence rates for both types of boundary conditions.

math.AP↗

arXiv2021

Long-time behavior of solutions to the M1 model with boundray effect

In this paper, we are concerned with the asymptotic behavior of solutions of M1 model on quadrant. From this model, combined with damped compressible Euler equations, a more general system is introduced. We show that the solutions to the initial boundary value problem of this system globally exist and tend time-asymptotically to the corresponding nonlinear parabolic equation governed by the related Darcy's law. Compared with previous results on compressible Euler equations with damping obtained by Nishihara and Yang in [24], and Marcati, Mei and Rubino in [16], the better convergence rates are obtained. The approach adopted is based on the technical time-weighted energy estimates together with the Green's function method.

math.AP↗

arXiv2021

Convergence to nonlinear diffusion waves for solutions of M1 model

In this paper, we are concerned with the asymptotic behavior of solutions of M1 model proposed in the radiative transfer fields. Starting from this model, combined with the compressible Euler equation with damping, we introduce a more general system. We rigorously prove that the solutions to the Cauchy problem of this system globally exist and time-asymptotically converge to the shifted nonlinear diffusion waves whose profile is self-similar solution to the corresponding parabolic equation governed by the classical Darcy's law. Moreover, the optimal convergence rates are also obtained. Compared with previous results obtained by Nishihara, Wang and Yang in [29], we have a weaker and more general condition on the initial data, and the conclusions are more sharper. The approach adopted in the paper is the technical time-weighted energy estimates with the Green function method together.

math.AP↗