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arXiv · 1604.07643

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

Dongho Chae·Joerg Wolf
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Abstract

In this paper we prove three different Liouville type theorems for the steady Navier-Stokes equations in $\Bbb R^3$. In the first theorem we improve logarithmically the well-known $L^{\frac92} (\Bbb R^3)$ result. In the second theorem we present a sufficient condition for the trivially of the solution($v=0$) in terms of the head pressure, $Q=\frac12 |v|^2 +p$. 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 $v=0$.

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Dongho Chae, Joerg Wolf. 2016-04-26. On Liouville type theorems for the steady Navier-Stokes equations in $\Bbb R^3$. https://arxiv.org/abs/1604.07643

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