On the continuity of solutions to advection-diffusion equations with slightly super-critical divergence-free drifts

Mihaela Ignatova

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We address the regularity of solutions to elliptic and parabolic equations of the form -δu + b - ∇u = 0 and ut - Δu + b - ∇u = 0 with divergence-free drifts b. We are particularly interested in the case when the drift velocity b is assumed to be at the supercritical regularity level with respect to the natural scaling of the equations. Using Harnack-type inequalities obtained in our previous works [7] and [8], we prove the uniform continuity of solutions when the drift b lies in a slightly supercritical logarithmic Morrey spaces.

Original languageEnglish (US)
Pages (from-to)81-86
Number of pages6
JournalAdvances in Nonlinear Analysis
Volume3
Issue number2
DOIs
StatePublished - May 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Drift-diffusion equations
  • Harnack inequality
  • Regularity

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