Hao Liu

Rigidity of Stationary Navier-Stokes Solutions with Transverse bound in Dimensions Five and Higher

For $n\geq5$, let $(u,p)$ be a smooth solution of the stationary incompressible Navier-Stokes equations in $\R^n\setminus\{x'=0\}$, where $\{x'=0\}$ is the $x_n$-axis. We prove that the scale-invariant transverse bound $|u(x)|\leq C |x'|^{-1}$ forces $u\equiv0$. This result relies on a quantitative local regularity the...