Global regularity for the 2D micropolar Rayleigh-B\'{e}nard convection system with velocity zero dissipation and temperature critical dissipation

TL;DR

This paper proves the global regularity of solutions for a 2D micropolar Rayleigh-Bénard convection system with specific dissipation properties, advancing understanding of fluid dynamics with micro-rotation effects.

Contribution

It introduces a novel combined quantity and employs Littlewood-Paley decomposition to establish global regularity for this complex convection system.

Findings

Global regularity of solutions is proven.

The method applies to systems with velocity zero dissipation.

The approach advances mathematical understanding of micropolar convection.

Abstract

This paper studies the global regularity problem for the 2D micropolar Rayleigh-B\'{e}nard convection system with velocity zero dissipation, micro-rotation velocity Laplace dissipation and temperature critical dissipation. By introducing a combined quantity and using the technique of Littlewood-Paley decomposition, we establish the global regularity result of solutions to this system.