A new sufficient condition for local regularity of a suitable weak solution to the MHD equations

We assume that Omega is either the whole space R-3 or a half-space or a smooth bounded or exterior domain in R-3, T > 0 and (u, b, p) is a suitable weak solution of the MHD equations in Omega x (0, T). We show that (x(0), t(0)) is an element of Omega x (0, T) is a regular point of the solution (u, b, p) if the limit inferior (for t -> t(0)-) of the sum of the L-3-norms of u and b over an arbitrarily small ball B-rho(x(0)) is less than infinity. (C) 2021 Elsevier Inc. All rights reserved.