Global existence of strong solutions to micropolar equations in cylindrical domains

TL;DR

This paper proves the global existence of strong solutions to micropolar equations in cylindrical domains without restrictions on initial data magnitude, assuming limited variation in the axial direction.

Contribution

It establishes the existence of strong solutions in cylindrical domains for micropolar equations without size restrictions on initial data.

Findings

Global strong solutions exist in cylindrical domains

No restrictions on initial and external data magnitude

Solutions require limited variation in the axial direction

Abstract

The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in $\mathbb{R}^3$. We do not impose any restrictions on the magnitude of the initial and external data but we require that they cannot change in the $x_3$-direction too fast.