On Liouville type theorems for the steady Navier-Stokes equations in ${\mathbb{R}}^3$

Abstract

In this paper we prove three different Liouville type theorems for the steady Navier-Stokes equations in ${\mathbb{R}}^3$. In the first theorem we improve logarithmically the well-known $L^{\frac{9}{2}}({\mathbb{R}}^3)$ result. In the second theorem we present a sufficient condition for the trivially of the solution($v=0$) in terms of the head pressure, $Q=\frac{1}{2}|v{|}^2+p$. The imposed integrability condition here has the same scaling property as the Dirichlet integral. In the last theorem we present Fubini type condition, which guarantee $v=0$.

arXiv comment17 pages

Cited by in corpus (4)

• Remarks on Liouville Type Theorems for Steady-State Navier-Stokes Equations
• A Liouville Type Theorem for Steady-State Navier-Stokes Equations
• Sufficient conditions on Liouville type theorems for the 3D steady Navier-Stokes equations
• Remarks on Liouville type theorems for the 3D steady axially symmetric Navier-Stokes equations