Large time existence of strong solutions to micropolar equations in cylindrical domains

TL;DR

This paper proves the existence of unique strong solutions to the micropolar equations in cylindrical domains under Navier boundary conditions, given small initial and external data changes, extending fluid dynamics models.

Contribution

It establishes the first existence and uniqueness results for strong solutions of micropolar equations in cylindrical domains with Navier boundary conditions.

Findings

Existence of strong solutions under small data assumptions

Uniqueness of solutions for finite time intervals

Extension of fluid models to micropolar equations in cylindrical geometries

Abstract

We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the fluid into account. We prove that under certain smallness assumption on the rate of change of the initial data and the external data there exists a unique and strong solution for any finite time $T$.