The initial value problem for motion of micropolar fluids with heat conduction in Banach spaces

TL;DR

This paper studies the initial value problem for micropolar fluids with heat conduction, proving existence and uniqueness of solutions in Banach spaces using analytic semigroup theory, with results on local and global solutions.

Contribution

It establishes the existence, uniqueness, and regularity of solutions for the micropolar fluid system with heat conduction in a Banach space framework, extending previous results.

Findings

Unique local mild solutions for general initial data.

Global solutions for small initial data.

Conditions under which solutions are strong or classical.

Abstract

We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.