Global regularity to the 3D Cauchy problem of inhomogeneous magnetic Bénard equations with vacuum

Abstract

This paper deals with the Cauchy problem of 3D inhomogeneous incompressible magnetic Bénard equations. Through some time-weighted a priori estimates, we prove the global existence of strong solution provided that the upper boundedness of initial density and initial magnetic field satisfy some smallness condition. Furthermore, we also obtain large time decay rates of the solution.

Keywords

• inhomogeneous case
• magnetic bénard equations
• global regularity
• decay estimates