142 citations · 1.3k across the 62 of their papers we have counts for
3 papers · 2 filters
On the loss of continuity for super-critical drift-diffusion equations
Luis Silvestre, Vlad Vicol, Andrej Zlatos
We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts, that become discontinuous in finite time. We consider…
Global well-posedness of slightly supercritical active scalar equations
Michael Dabkowski, Alexander Kiselev, Luis Silvestre +1
The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasi-geostrophic (SQG) and Burgers e…
On a singular incompressible porous media equation
Susan Friedlander, Francisco Gancedo, Weiran Sun +1
In this paper we study a singularly modified version of the incompressible porous media equation. We investigate the implications for the local well-posedness of the equations by m…