A crypto-regularity result for the micropolar fluids equations

TL;DR

This paper demonstrates a gain in integrability for weak solutions of micropolar fluid equations using Morrey spaces, highlighting the potential for improved regularity analysis in PDEs through Lebesgue space frameworks.

Contribution

It introduces a novel approach to analyze regularity in micropolar fluid equations by employing Morrey spaces, allowing separate treatment of the two variables.

Findings

Gain of integrability for weak solutions

Use of Morrey spaces as a regularity framework

Separate analysis of variables in micropolar equations

Abstract

In the analysis of PDEs, regularity of often measured in terms of Sobolev, H{\"o}lder, Besov or Lipschitz spaces, etc. However, sometimes a gain of regularity can also be expressed just in terms of Lebesgue spaces, by passing from a singular setting to a less singular one. In this article we will obtain a gain of integrability for weak solutions of the micropolar fluid equations using as general framework Morrey spaces, which is a very useful language to study regularity in PDEs. An interesting point is that the two variables of the micropolar fluid equations can be studied separately.