Remarks on a fractional diffusion transport equation with applications to the dissipative quasi-geostrophic equation

Abstract

In this article I study Hölder regularity for solutions of a transport equation based in the dissipative quasi-geostrophic equation. Following a recent idea of A. Kiselev and F. Nazarov, I will use the molecular characterization of local Hardy spaces in order to obtain information on Hölder regularity of such solutions. This will be done by following the evolution of molecules in a backward equation.

27 pages

References in corpus (4)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• On the global well-posedness of the critical quasi-geostrophic equation
• On the critical dissipative quasi-geostrophic equation
• A variation on a theme of Caffarelli and Vasseur

Cited by in corpus (3)

• On the loss of continuity for super-critical drift-diffusion equations
• Dissipative models generalizing the 2D Navier-Stokes and the surface quasi-geostrophic equations
• Generalized surface quasi-geostrophic equations with singular velocities