Abstract
We use De Giorgi techniques to prove Hölder continuity of weak solutions to a class of drift-diffusion equations, with L2 initial data and divergence free drift velocity that lies in Lt∞BMOx−1. We apply this result to prove global regularity for a family of active scalar equations which includes the advection–diffusion equation that has been proposed by Moffatt in the context of magnetostrophic turbulence in the Earthʼs fluid core.
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