On a 1D transport equation with nonlocal velocity and supercritical dissipation

Abstract

We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global regularity for solutions when dissipation is slightly supercritical. Both results utilize a nonlocal maximum principle.

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global well-posedness of slightly supercritical active scalar equations

Cited by in corpus (2)

• Global well-posedness of slightly supercritical active scalar equations
• On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion