Communications in Mathematical Sciences

Volume 21 (2023)

Number 8

Global strong solutions to the compressible Navier–Stokes system with potential temperature transport

Pages: 2247 – 2260

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n8.a8

Authors

Xiaoping Zhai (School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, China)

Yongsheng Li (School of Mathematics, South China University of Technology, Guangzhou, China)

Fujun Zhou (School of Mathematics, South China University of Technology, Guangzhou, China)

Abstract

We study the global strong solutions to the compressible Navier–Stokes system with potential temperature transport in $\mathbb{R}^n$. Different from the Navier–Stokes–Fourier system, the pressure being a nonlinear function of the density and the potential temperature, we can not exploit the special quasi-diagonalization structure of this system to capture any dissipation of the density. Some new ideas and delicate analysis involving high or low frequency decomposition in the Besov spaces have to be made to close the energy estimates.

Keywords

global solutions, compressible Navier–Stokes equations, Besov spaces

2010 Mathematics Subject Classification

35M11, 35Q30, 35Q35

Full Text (PDF format)

This research is supported by the NSFC key project under the grant number 11831003; by the NSFC under the grant numbers 12271179, 11971356, 11601533, and 11571118; by the Science and Technology Program of Shenzhen under the grant number 20200806104726001; by the Fundamental Research Funds for the Central Universities under the grant numbers 2019MS110 and 2019MS112; and by the Foundation for Basic and Applied Basic Research of Guangdong under the grant numbers 2022A1515011977 and 2022A1515012097.

Received 18 July 2021

Received revised 21 March 2023

Accepted 2 April 2023

Published 15 November 2023