Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation

Charles L. Fefferman, José L. Rodrigo

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.

Original languageEnglish (US)
Pages (from-to)123-162
Number of pages40
JournalArchive for Rational Mechanics and Analysis
Volume218
Issue number1
DOIs
StatePublished - Oct 27 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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