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

TL;DR

This paper establishes the existence of global strong solutions for the compressible Navier-Stokes equations with potential temperature transport, addressing nonlinear pressure dependencies without relying on traditional quasi-diagonalization techniques.

Contribution

It introduces new analytical methods involving high and low frequency decomposition in Besov spaces to handle the nonlinear pressure terms and prove global solutions.

Findings

Proved global strong solutions exist under certain conditions.

Developed novel analytical techniques for nonlinear pressure terms.

Extended understanding of compressible Navier-Stokes with temperature transport.

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 is 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 idea and delicate analysis involved in high or low frequency decomposition in the Besov spaces have to be made to close the energy estimates.