Global regularity for the 2D micropolar Rayleigh–Bénard problem with partial dissipation

Abstract

This paper is devoted to the study of the global regularity problem to the 2D micropolar Rayleigh–Bénard problem with only partial velocity dissipation and micro-rotational dissipation in R2. By fully exploiting the special structure of the system and using the delicate energy methods, we establish the global well-posedness of classical solutions for this system.