On the Liouville type theorems for the stationary Navier-Stokes equations in R3

초록

In this paper we prove Liouville type theorems for the stationary solution to the Navier-Stokes equations in R3. Let (u,p) a smooth stationary solution to the Navier-Stokes equations in R3, satisfying ∫R|∇u|2dx<+∞, and Q=[Formula presented]|u|2+p is its head pressure, which vanishes at infinity. Then, we prove various Liouville type theorems, using the function ξ satisfying the Osgood criterion. These theorems improve some of previously known results. The proofs use the level set methods and the coarea formula. © 2025 Elsevier Inc.

키워드