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On the Loss of Continuity for Super-Critical Drift-Diffusion Equations |
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| Authors: | Luis Silvestre Vlad Vicol Andrej Zlatoš |
| Institution: | 1. Department of Mathematics, The University of Chicago, Chicago, IL, USA 2. Department of Mathematics, Princeton University, Princeton, NJ, USA 3. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA |
| Abstract: | 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 classical as well as fractional diffusion. However, in the case of classical diffusion and time-independent drifts, we prove that solutions satisfy a modulus of continuity depending only on the local L 1 norm of the drift, which is a super-critical quantity. |
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