Time Periodic Doubly Connected Solutions for the 3D Quasi-Geostrophic Model

DOI10.1137/22m1513666zbMath1527.35277arXiv2206.10197MaRDI QIDQ6086710

Joan Mateu, Taoufik Hmidi, Claudia I. Garcia

Publication date: 10 November 2023

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.10197

zbMATH Keywords

periodic solutionseigenvalue problemsbifurcation theory3D quasi-geostrophic equations

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs in connection with fluid mechanics (35Q35) General theory of rotating fluids (76U05) Bifurcations in context of PDEs (35B32) PDEs in connection with geophysics (35Q86)

Cites Work

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• Doubly connected V-states for the generalized surface quasi-geostrophic equations
• Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations
• Degenerate bifurcation of the rotating patches
• Bifurcation of rotating patches from Kirchhoff vortices
• An analytical and numerical study of steady patches in the disc
• Existence of corotating and counter-rotating vortex pairs for active scalar equations
• Motions of vortex patches
• Bifurcation theory. An introduction with applications of PDEs
• Uniformly rotating analytic global patch solutions for active scalars
• Uniformly rotating smooth solutions for the incompressible 2D Euler equations
• Imperfect bifurcation for the quasi-geostrophic shallow-water equations
• On the existence of stationary patches
• Global regularity for vortex patches
• Perturbation theory for linear operators.
• Derivation of quasi-geostrophic potential vorticity equations
• Steady asymmetric vortex pairs for Euler equations
• On the V-states for the generalized quasi-geostrophic equations
• Vortex patches choreography for active scalar equations
• Symmetry in stationary and uniformly rotating solutions of active scalar equations
• Time periodic solutions for 3D quasi-geostrophic model
• Non uniform rotating vortices and periodic orbits for the two-dimensional Euler equations
• On rotating doubly connected vortices
• Boundary regularity of rotating vortex patches
• Bifurcation from simple eigenvalues
• Vorticity and Incompressible Flow
• Doubly Connected $V$-States for the Planar Euler Equations
• Persistance de structures géométriques dans les fluides incompressibles bidimensionnels
• Global Smooth Solutions for the Inviscid SQG Equation
• Validity of the Quasigeostrophic Model for Large-Scale Flow in the Atmosphere and Ocean
• Three-dimensional quasi-geostrophic vortex equilibria with -fold symmetry
• The stability and nonlinear evolution of quasi-geostrophic toroidal vortices
• The quasi-geostrophic ellipsoidal vortex model
• Global Bifurcation of Rotating Vortex Patches
• Kármán vortex street in incompressible fluid models
• The stability of quasi-geostrophic ellipsoidal vortices
• An exact steadily rotating surface quasi-geostrophic elliptical vortex
• High-field limit for the Vlasov-Poisson-Fokker-Planck system.
• Illposedness of \(C^2\) vortex patches
• Time quasi-periodic vortex patches of Euler equation in the plane

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