Global well-posedness for three-dimensional compressible viscous micropolar and heat-conducting fluids with vacuum at infinity and large oscillations

TL;DR

This paper proves the global existence and uniqueness of strong solutions for three-dimensional compressible viscous micropolar fluids with heat conduction and vacuum at infinity, allowing large initial oscillations and mass.

Contribution

It extends previous results by establishing global well-posedness under broader conditions, including large initial mass and vacuum at infinity.

Findings

Global existence and uniqueness of strong solutions

Initial mass can be arbitrarily large

Vacuum at infinity is permitted

Abstract

We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence and uniqueness of strong solutions under some smallness condition depending only on the parameters appeared in the system and the initial mass. In particular, the initial mass can be arbitrarily large. This improves our previous work [23]. Moreover, we also generalize the result [13] to the case that vacuum is allowed at infinity.