TIME PERIODIC DOUBLY CONNECTED SOLUTIONS FOR THE 3D QUASI-GEOSTROPHIC MODEL

Claudia García, Taoufik Hmidi, Joan Mateu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we construct time periodic doubly connected solutions for the three-dimensional quasi-geostrophic model in the patch setting. More specifically, we prove the existence of nontrivial m-fold doubly connected rotating patches bifurcating from a generic doubly connected revolution shape domain with higher symmetry m \geq m0 and m0 large enough. The linearized matrix operator at the equilibrium state has variable and singular coefficients and its spectral analysis is performed via the approach devised in [C. Garc1́a, T. Hmidi, and J. Mateu, Comm. Math. Phys., 390 (2022), pp. 617-756], where a suitable symmetrization was introduced. New difficulties emerge due to the interaction between the surfaces making the spectral problem richer and involved.

Original languageEnglish (US)
Pages (from-to)6133-6193
Number of pages61
JournalSIAM Journal on Mathematical Analysis
Volume55
Issue number6
DOIs
StatePublished - Dec 2023

Keywords

  • 3D quasi-geostrophic equations
  • bifurcation theory
  • eigenvalue problems
  • periodic solutions

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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