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Global Solutions for the Generalized SQG Patch Equation

  • Diego Córdoba
  • Javier Gómez-Serrano
  • Alexandru D. IonescuEmail author
Article
  • 13 Downloads

Abstract

We consider the inviscid generalized surface quasi-geostrophic equation (gSQG) in a patch setting, where the parameter \({\alpha \in (1,2)}\). The cases \({\alpha = 0}\) and \({\alpha = 1}\) correspond to 2d Euler and SQG respectively, and our choice of the parameter \({\alpha}\) 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.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de Ciencias MatemáticasMadridSpain
  2. 2.Princeton UniversityPrincetonUSA

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