A logarithmically improved regularity criterion for the 3D Hall-MHD equations in Besov spaces with negative indices

Abstract

In this paper we consider the three dimensional (3D) incompressible Hall-magnetohydrodynamic equations (Hall-MHD). It is proved that the local smooth solution can be continued beyond time T provided that the velocity u and the magnetic field B satisfyfor . As a consequence, this result extend the previous result.