Landau-solution classification conjecture for critical stationary Navier–Stokes flows

Let $u$ be a vector field on $\boldsymbol{\mathbb{R}}^3\setminus\{0\}$ satisfying

$$|u(x)|\leq \frac{C}{|x|}$$

for every $x\neq 0$, where $C$ is a sufficiently large constant. Suppose that $u$ is a very weak solution of the stationary incompressible Navier–Stokes equations on $\boldsymbol{\mathbb{R}}^3\setminus\{0\}$, in the sense of the preceding definition with drift $b=u$.

Landau-solution classification conjecture. Then $u$ is one of the Landau solutions, which are minus-one homogeneous and axisymmetric without swirl.

This is an open problem concerning the classification of critical, scale-invariant stationary Navier–Stokes solutions with an isolated singularity. Landau solutions provide the known explicit examples, while the conjecture asserts that no other solutions with the stated pointwise bound exist.