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math.AP2012★ 54 cited
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…
math.AP2012★ 52 cited
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…