Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum

TL;DR

This paper proves the global existence and uniqueness of classical solutions for 3D compressible micropolar viscous flows with large oscillations and vacuum, and analyzes their long-term behavior.

Contribution

It establishes the existence of global classical solutions under small initial energy conditions, even with large oscillations and vacuum states, which is a significant extension of prior results.

Findings

Existence of unique global classical solutions

Solutions exhibit specific large-time behavior

Initial vacuum states are permitted

Abstract

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large oscillations, the initial density may allowed to contain vacuum states. Furthermore, the large-time behavior of the solution is obtained.