On the Differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion

Abstract

We investigate the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion at either supercritical or critical type cases. Under the suitable conditions on the drift velocity and the forcing term in terms of the spatial Hölder regularity, we prove that the vanishing viscosity solution is differentiable with some Hölder continuous derivatives for any positive time.

24 pages. Submitted

References in corpus (4)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation
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Cited by in corpus (1)

• On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion