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Research Article | Open Access

On Liouville-type theorem for the stationary compressible Navier–Stokes equations in R 3

Caifeng Liu1, Pan Liu2( )
School of Mathematics, Northwest University, Xi'an 710127, Shaanxi, China
School of Mathematics and Statistics, Yulin University, Yulin 719000, Shaanxi, China
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Abstract

In this paper, we study the Liouville-type theorem for the stationary barotropic compressible Navier–Stokes equations in R 3 . Based on a fairly general framework of a kind of local mean oscillations integral and Morrey spaces, we prove that the velocity and the density of the flow are trivial without any integrability assumption on the gradient of the velocity.

Keywords

Liouville-type theoremcompressible Navier–Stokes equaitonsbarotropiclocal mean oscillations integralMorrey spaces

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Electronic Research Archive
Volume 32 Issue 1,
January 2024
Pages 386-404
DOI: 10.3934/era.2024019

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Liu C, Liu P. On Liouville-type theorem for the stationary compressible Navier–Stokes equations in R 3 . Electronic Research Archive, 2024, 32(1): 386-404. https://doi.org/10.3934/era.2024019

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Received: 15 October 2023
Revised: 06 December 2023
Accepted: 18 December 2023
Published: 28 December 2023
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)