# A remark on the Liouville problem for stationary Navier-Stokes equations in Lorentz and Morrey spaces

## TL;DR

This paper proves Liouville type theorems for stationary Navier-Stokes equations in Lorentz and Morrey spaces, improving recent results and encompassing well-known special cases.

## Contribution

It introduces new Liouville theorems for stationary Navier-Stokes equations assuming velocity fields in Lorentz and Morrey spaces, extending previous work.

## Key findings

- Liouville theorems established for Lorentz spaces
- Results include Morrey spaces as a broader setting
- Theorems generalize and improve upon recent findings

## Abstract

The Liouville problem for the stationary Navier-Stokes equations on the whole space is a challenging open problem who has know several recent contributions. We prove here some Liouville type theorems for these equations provided the velocity field belongs to some Lorentz spaces and then in the more general setting of Morrey spaces. Our theorems correspond to a improvement of some recent result on this problem and contain some well-known results as a particular case.