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

TL;DR

This paper proves Liouville theorems ensuring the uniqueness of trivial solutions for stationary 3D Navier-Stokes equations under certain Lebesgue and Morrey space conditions, advancing understanding of solution uniqueness in fluid dynamics.

Contribution

It establishes new Liouville theorems for stationary Navier-Stokes equations using Lebesgue and Morrey space hypotheses, extending previous results on solution uniqueness.

Findings

Trivial solution U=0 is unique under specified space conditions

Liouville theorems are proved for stationary Navier-Stokes equations

Results contribute to understanding solution uniqueness in fluid mechanics

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.