Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces

2018/06/08 by Chamorro, Diego, Jarrin, Oscar, Lemarié-Rieusset, Pierre-Gilles · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.03003

Abstract

Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations and under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution U = 0 is the unique solution. This type of results are known as Liouville theorems.

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