Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space

Abstract

We prove local regularity condition for a suitable weak solution to 3D MHD equations. Precisely, if a solution satisfies $u, b \in L^{\infty}(-(\frac{4}{3})^2, 0;L^{3, q}(B_{\frac{3}{4}}))$, $q\in (3, \infty)$ in Lorentz space, then $(u, b)$ is Hölder continuous in the closure of the set $Q_{\frac{1}{2}}$.

Keywords

• local regularity condition
• suitable weak solution
• 3d mhd equations