Osgood's Lemma and Some Results for the Slightly Supercritical 2D Euler Equations for Incompressible Flow

Tarek Mohamed Elgindi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We investigate the (slightly) super-critical two-dimensional Euler equations. The paper consists of two parts. In the first part we prove well-posedness in Cs spaces for all s > 0. We also give growth estimates for the Cs norms of the vorticity for 0 < s ≦ 1. In the second part we prove global regularity for the vortex patch problem in the super-critical regime. This paper extends the results of Chae et al. where they prove well-posedness for the so-called LogLog-Euler equation. We also extend the classical results of Chemin and Bertozzi-Constantin on the vortex patch problem to the slightly supercritical case. Both problems we study in the setting of the whole space.

Original languageEnglish (US)
Pages (from-to)965-990
Number of pages26
JournalArchive for Rational Mechanics and Analysis
Volume211
Issue number3
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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