Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocities

Details Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocities Higher regularity of Holder continuous solutions of parabolic equations with singular drift velocities

2011-02-02

arxiv.org/abs/1102.0585v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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