On the Loss of Continuity for Super-Critical Drift-Diffusion Equations

Luis Silvestre, Vlad Vicol, Andrej Zlatoš

Research output: Contribution to journalArticle

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 L1 norm of the drift, which is a super-critical quantity.

Original languageEnglish (US)
Pages (from-to)845-877
Number of pages33
JournalArchive for Rational Mechanics and Analysis
Volume207
Issue number3
DOIs
StatePublished - Jan 1 2013

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Drift-diffusion Equations
Fractional Diffusion
Divergence-free
L1-norm
Modulus of Continuity
Two Dimensions

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

On the Loss of Continuity for Super-Critical Drift-Diffusion Equations. / Silvestre, Luis; Vicol, Vlad; Zlatoš, Andrej.

In: Archive for Rational Mechanics and Analysis, Vol. 207, No. 3, 01.01.2013, p. 845-877.

Research output: Contribution to journalArticle

Silvestre, Luis ; Vicol, Vlad ; Zlatoš, Andrej. / On the Loss of Continuity for Super-Critical Drift-Diffusion Equations. In: Archive for Rational Mechanics and Analysis. 2013 ; Vol. 207, No. 3. pp. 845-877.
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