Global well-posedness for the 2D micropolar Rayleigh-B\'{e}nard convection problem

TL;DR

This paper proves the global well-posedness of the 2D micropolar Rayleigh-Bénard convection system without velocity dissipation, providing conditions for solution existence and blow-up criteria.

Contribution

It establishes the global well-posedness for the 2D micropolar Rayleigh-Bénard convection problem without velocity dissipation, including local existence and blow-up criteria.

Findings

Proved local well-posedness of smooth solutions.

Established blow-up criterion based on temperature gradient.

Demonstrated global well-posedness of the system.

Abstract

In this article, we study the Cauchy problem to the micropolar Rayleigh-B\'{e}nard convection problem without velocity dissipation in two dimension. We first prove the local well-posedness of a smooth solution, and then establish a blow up criterion in terms of the gradient of scalar temperature field. At last, we obtain the global well-posedness to the system.