Author

Guo-Xu Yang

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Preprint Aug 2026

Critical Morrey Rigidity and Removable Singularities for Five-Dimensional Stationary Navier-Stokes Flows

We prove a critical Morrey rigidity theorem for the five-dimensional stationary Navier--Stokes equations. More precisely, every smooth solution on $\mathbb R^5\setminus\{0\}$ satisfying \[ \sup_{R>0}R^{-2}\int_{B_R}|u|^3\,dx<\infty \] is identically zero, up to an additive constant in the pressure. This replaces the po...

Yu-Bo Chen, Wen-Dong Wang, Xiao Wang et al. · 2 citations

Preprint Sep 2026

Regular Solutions of the Stationary Navier-Stokes Equations in Arbitrarily High Dimensions

Recently, the existence of regular solutions $(u,p)$ to the stationary incompressible Navier--Stokes equations on $\mathbb R^n$ with bounded compactly supported forces $f$ for $5\le n\le15$ was established by Li--Yang (Comm. Math. Phys., 2022). However, it is still unknown whether there exists a regular solution for di...

Wen-Dong Wang, Guo-Xu Yang · 2 citations · ⚡2