5 problems

Consider the stationary Navier–Stokes system in $\mathbb{R}^3$: … Here $u$ is the velocity vector field, $\pi$ is the pressure, and $\dot{H}^1(\mathbb{R}^3)$ denotes the homogeneou…

Let $v$ be a vector field satisfying the assumptions of the Liouville conjecture for stationary Navier–Stokes fields. In addition, suppose that $v$ is the restriction to…

Let $v$ be a vector field on $\mathbb R^{3}$, with pressure $p$, satisfying the stationary Navier–Stokes system … where $\nu>0$, together with … and…

Let $u$ and $p$ be smooth functions on $\mathbb R^3$ satisfying the stationary Navier–Stokes system … with $u(x)\to 0$ as $|x|\to\infty$. The condition $u\in L^{9/2}(\mathbb R^3)$…

Let $u$ be a solution of the stationary Navier–Stokes equations with zero force in $\mathbb{R}^3\setminus\{0\}$ satisfying the bound … for some $C_*>0$. A Landau-solution conjectur…