Higher regularity of Holder continuous solutions of parabolic equations   with singular drift velocities
  Motivated by an equation arising in magnetohydrodynamics, we prove that Holder continuous weak solutions of a nonlinear parabolic equation with singular drift velocity are classical solutions. The result is proved using the space-time Besov spaces introduced by Chemin and Lerner, combined with energy estimates, without any minimality assumption on the Holder exponent of the weak solutions. 
Susan Friedlander and Vlad Vicol
math.AP