, Volume 20, Issue 4, pp 695-700

On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations

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Abstract

In this paper, we consider the blow-up of smooth solutions to the 3D ideal MHD equations. Let (u, b) be a smooth solution in (0, T). It is proved that the solution (u, b) can be extended after t = T if \( {\left( {\nabla \times u,\nabla \times b} \right)} \in L^{1} {\left( {0,T;\ifmmode\expandafter\dot\else\expandafter\.\fi{B}^{0}_{{\infty ,\infty }} } \right)} \) . This is an improvement of the result given by Caflisch, Klapper, and Steele [3].