Initial-boundary value problem for 2D micropolar equations without angular viscosity

TL;DR

This paper proves the existence and uniqueness of global weak solutions for 2D micropolar equations without angular viscosity, by exploiting system structure and establishing high-order estimates with an auxiliary field.

Contribution

It introduces a novel approach to analyze 2D micropolar equations without angular viscosity, providing a framework for global weak solutions.

Findings

Existence of unique global weak solutions

High order estimates established using auxiliary fields

Method applicable to similar micropolar systems

Abstract

This paper concerns the initial-boundary value problem to 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global weak solution. The main idea of this paper is to fully exploit the structure of this system and establish high order estimates via introducing an auxiliary field which is at the energy level of one order lower than micro-rotation.