ON APPROXIMATE SOLUTIONS FOR A CLASS OF SEMILINEAR FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS IN BANACH SPACES
Fixed Point Theory and Applications. Springer International Publishing. Том 2017. 2017.
The paper deals with the 3D incompressible MHD equations and aims at improving a regularity criterion in terms of the horizontal gradient of velocity and magnetic field. It is proved that the weak solution (u, b) becomes regular provided that (Formula Presented.) The result is an extension of regularity criterion for 3D Navier–Stokes equations in Besov space due to Fang and Qian (Commun Pure Appl Anal 13:585–603, 2014) [see also (Ni et al. in J Math Anal Appl 396:108–118, 2012)]. © 2017, Springer International Publishing AG, part of Springer Nature.