Hölder continuity for a drift-diffusion equation with pressure

Luis Silvestre, Vlad Vicol

Research output: Contribution to journalArticle

Abstract

We address the persistence of Hölder continuity for weak solutions of the linear drift-diffusion equation with nonlocal pressureu t+b·∇ u-Δu=∇p, Δu=0 on [0,∞) × ℝn, with n≥2. The drift velocity b is assumed to be at the critical regularity level, with respect to the natural scaling of the equations. The proof draws on Campanato's characterization of Hölder spaces, and uses a maximum-principle-type argument by which we control the growth in time of certain local averages of u. We provide an estimate that does not depend on any local smallness condition on the vector field b, but only on scale invariant quantities.

Original languageEnglish (US)
Pages (from-to)637-652
Number of pages16
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume29
Issue number4
DOIs
StatePublished - Jan 1 2012

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Drift-diffusion Equations
Maximum principle
Scale Invariant
Maximum Principle
Persistence
Weak Solution
Linear equation
Vector Field
Regularity
Scaling
Estimate

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Cite this

Hölder continuity for a drift-diffusion equation with pressure. / Silvestre, Luis; Vicol, Vlad.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 29, No. 4, 01.01.2012, p. 637-652.

Research output: Contribution to journalArticle

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