3 problems

Du–Guo rigidity conjecture. Every bounded solution $u$ still depends only on $x_N$ and is monotone increasing in $x_N$, with

Let $Q_-^+=\mathbb R^3_+\times(-\infty,0)$, where $\mathbb R^3_+=\{x=(x_1,x_2,x_3)\in\mathbb R^3:x_3>0\}$. A mild bounded ancient solution is a bounded ancient solution of the Navi…

Let $u$ be a mild bounded ancient solution of the Navier–Stokes equations in the half space $\mathbb R^3_+$, meaning a bounded ancient solution satisfying the pressure decompositio…