On the inviscid Boussinesq system with rough initial data

Zineb Hassainia, Taoufik Hmidi

Research output: Contribution to journalArticlepeer-review

Abstract

We deal with the local well-posedness theory for the two-dimensional inviscid Boussinesq system with rough initial data of Yudovich type. The problem is in some sense critical due to some terms involving Riesz transforms in the vorticity-density formulation. We give a positive answer for a special sub-class of Yudovich data including smooth and singular vortex patches. For the latter case we assume in addition that the initial density is constant around the singular part of the patch boundary.

Original languageEnglish (US)
Pages (from-to)777-809
Number of pages33
JournalJournal of Mathematical Analysis and Applications
Volume430
Issue number2
DOIs
StatePublished - Oct 15 2015

Keywords

  • 2D inviscid Boussinesq system
  • Local well-posedness
  • Vortex patches

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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