Conditional Regularity of Weak Solutions to the 3D Magnetic Bénard Fluid System

Abstract

This paper concerns about the regularity conditions of weak solutions to the magnetic Bénard fluid system in $\mathbb{R}^3$. We show that a weak solution $(u,b,θ)(·,t)$ of the 3D magnetic Bénard fluid system defined in $[0,T),$ which satisfies some regularity requirement as $(u,b,θ),$ is regular in $\mathbb{R}^3×(0,T)$ and can be extended as a $C^∞$ solution beyond $T$.