Global well-posedness of dissipative quasi-geostrophic equations in critical spaces

DOI10.1090/S0002-9939-07-09060-0zbMath1175.35108MaRDI QIDQ5429447

Hantaek Bae

Publication date: 30 November 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

quasi-geostrophic equationsglobal well-posedness in critical Besov spaces

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (13)

Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces ⋮ Well-posedness and blow-up of solutions for the 2D dissipative quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces ⋮ On the second iterate for critically diffusive active scalar equations ⋮ Gevrey Class Regularity for the 2D Subcritical Dissipative Quasi-geostrophic Equation in Critical Fourier-Besov-Morrey Spaces ⋮ Global well-posedness for the critical dissipative quasi-geostrophic equations in \(L^\infty\) ⋮ Gevrey regularity for a class of dissipative equations with applications to decay ⋮ Global existence of the two-dimensional QGE with sub-critical dissipation ⋮ On Gevrey regularity of the supercritical SQG equation in critical Besov spaces ⋮ Commutator estimate in terms of partial derivatives of solutions for the dissipative quasi-geostrophic equation ⋮ Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations ⋮ Commutator estimate and its application to regularity criteria of the dissipative quasi-geostrophic equation ⋮ Global well-posedness, Gevrey class regularity and large time asymptotics for the dissipative quasi-geostrophic equation in Fourier-Besov spaces ⋮ Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation

Cites Work

• Lower bounds for an integral involving fractional Laplacians and the generalized Navier-Stokes equations in Besov spaces
• A maximum principle applied to quasi-geostrophic equations
• Global well-posedness in the super-critical dissipative quasi-geostrophic equations
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations

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