Global Solutions for the Generalized SQG Patch Equation

Diego Córdoba, Javier Gómez-Serrano, Alexandru D. Ionescu

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We consider the inviscid generalized surface quasi-geostrophic equation (gSQG) in a patch setting, where the parameter α∈ (1 , 2). The cases α= 0 and α= 1 correspond to 2d Euler and SQG respectively, and our choice of the parameter α results in a velocity more singular than in the SQG case. Our main result concerns the global stability of the half-plane patch stationary solution, under small and localized perturbations. Our theorem appears to be the first construction of stable global solutions for the gSQG-patch equations. The only other nontrivial global solutions known so far in the patch setting are the so-called V-states, which are uniformly rotating and periodic in time solutions.

Original languageEnglish (US)
Pages (from-to)1211-1251
Number of pages41
JournalArchive for Rational Mechanics and Analysis
Volume233
Issue number3
DOIs
StatePublished - Sep 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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