Global Regularity for the Inviscid Micropolar-Rayleigh-Bénard Convection System With Nonlinear Thermal Diffusion

The present article explores the global well-posedness of the two-dimensional micropolar-Rayleigh–Bénard convection system without any dissipation in the velocity equation which means that the fluid is governed by the Euler equation forced by the angular rotation of the fluid and buoyancy force, precisely, we establish the global Sobolev regularity for this kind of system.