Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
arXiv:1007.1211 · doi:10.1016/j.anihpc.2011.01.002
Abstract
We use De Giorgi techniques to prove Hölder continuity of weak solutions to a class of drift-diffusion equations, with $L^2$ initial data and divergence free drift velocity that lies in $L_{t}^{\infty}BMO_{x}^{-1}$. 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 Earth's fluid core.
To appear in Annales de l'Institut Henri Poincare - Analyse non lineaire