THE ANISOTROPIC INTEGRABILITY LOGARITHMIC REGULARITY CRITERION FOR THE 3D MHD EQUATIONS

This study is devoted to investigating the regularity criterion of the 3D MHD equations in terms of pressure in the framework of anisotropic Lebesgue spaces. The result shows that if a weak solution (u, b) satisfies (1) integral(T)(0) parallel to parallel to partial derivative(3)pi(.,t)parallel to L-x3(gamma)parallel to L-x1 x2 alpha(q)/1+ ln (e + parallel to pi(., t)parallel to(L22) dt < infinity, where 1/gamma+2/q+2/alpha = lambda is an element of [2,3) and 3/lambda <= gamma <= alpha < 1/lambda-2, then (u, b) is regular at t = T, which improve the previous results on the MHD equations