Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocities
arXiv:1102.0585 · doi:10.1007/s00021-011-0054-1
Abstract
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.