On the Loss of Continuity for Super-critical Drift-diffusion Equations
نویسنده
چکیده
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 norm of the drift, which is a super-critical quantity.
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