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 $T$. |