A magnetic regularity criterion for the 2D MHD equations with velocity dissipation

In this paper we consider an initial value problem of the 2D MHD equations with velocity dissipation and without magnetic diffusion. We establish a new magnetic regularity criterion in terms of the magnetic field. In contrast to the magnetic regularity criterion del b is an element of L-1(0, T;BMO(R-2)), our regularity criterion integral(T)(0) (parallel to b circle times b(s)parallel to(B infinity,10(R2)) + parallel to b circle times b(s)parallel to(L2(R2))) ds < infinity is different; for example, our simplified regularity criterion integral(T)(0) parallel to b(s)parallel to(B infinity,1(R2)2) ds < infinity requires higher time integrability and lower regularity of space.