arXiv subjects

Zhuoni Chi

Publications and source records attributed to Zhuoni Chi.

3 recordsLinked to original sources

arXiv2026

Density of Forces Producing Navier--Stokes Blowup

We study the density of smooth external forces for which the three-dimensional Navier--Stokes equations lose classical regularity by a prescribed time $T>0$. Starting from the compact forced blowup solution of OpenAI, we construct a blowup solution near every given smooth solution while preserving its initial velocity. A smooth cutoff of a local vector potential makes the given velocity vanish near the support of a rescaled blowup solution. The two velocities then have no nonlinear interaction, and the resulting force remains smooth through the blowup time. For fixed viscosity and zero initial velocity, such forces are dense in the relative $L^1_tH^s_x$ topology on both $\mathbb{T}^3$ and $\mathbb{R}^3$ exactly when $s<1/2$.

math.AP↗

arXiv2026

Singular Forces on the Whole Space: Sobolev Density Thresholds and Energy Approximation

We derive whole-space distribution results from the established compact, smoothly forced Navier--Stokes blowup construction of OpenAI. For every fixed positive viscosity and deadline, smooth forces causing classical breakdown from rest on $\mathbb R^3$ are dense in the relative $L^1_tH^s_x$ topology exactly when $s<1/2$, and in the relative $L^2_tH^s_x$ topology exactly when $s<-1/2$. The positive results preserve every fixed initial velocity in $H^\infty_σ(\R^3)$. They follow from a compact divergence-free removal of a regular background, followed by exact insertion of a single whole-space singular packet. Separate critical estimates prove non-density; low spatial frequencies are controlled explicitly, without a periodic mean or a Poincaré inequality. The conclusions hold for spacetime-compact forces and for the rapidly decaying data class in the Clay formulation. We also obtain density in the usual completed energy-force spaces, strong energy-and-dissipation approximation of regular trajectories, and exact equality of cell observations on a prescribed finite family of whole-space grids. Initial-state spaces, forcing spaces and numerical error regularity are distinguished throughout. No claim of fixed-force instability, loss of weak existence or new formal verification is made.

math.AP↗

arXiv2026

Spherical representations of unitary groups at ramified places and the arithmetic inner product formula

In this article, we study admissible representations of even unitary groups over local fields, where the quadratic extension is ramified, with invariant vectors under the action of the stabilizer of a unimodular lattice and some properties of the corresponding integral model of unitary Shimura varieties. As a direct application, we are able to improve the arithmetic inner product formula so that the places with local root number $(-1)$ are allowed to be ramified.

math.NT↗