Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics

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 $L_t^{\infty }BM{O}_x^{-1}$. 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

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• On Divergence-free Drifts

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