On the regularity of a class of generalized quasi-geostrophic equations

DOI10.1016/j.jde.2011.04.018zbMath1292.76071arXiv1011.6214OpenAlexW2010395230MaRDI QIDQ640044

Liutang Xue, Chang Xing Miao

Publication date: 12 October 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6214

zbMATH Keywords

maximum principleregularity criterionglobal well-posedness

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) General theory of rotating fluids (76U05) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (22)

Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation ⋮ Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ Global regularity for several incompressible fluid models with partial dissipation ⋮ On the global regularity of two-dimensional generalized magnetohydrodynamics system ⋮ Uniform sparse domination and quantitative weighted boundedness for singular integrals and application to the dissipative quasi-geostrophic equation ⋮ Energy conservation for the generalized surface quasi-geostrophic equation ⋮ Long time behavior for the critical modified surface quasi-geostrophic equation ⋮ A uniform Besov boundedness and the well-posedness of the generalized dissipative quasi-geostrophic equation in the critical Besov space ⋮ Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation ⋮ The 2D Boussinesq equations with logarithmically supercritical velocities ⋮ Global well-posedness for a modified critical dissipative quasi-geostrophic equation ⋮ Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces ⋮ On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces ⋮ On Gevrey regularity of the supercritical SQG equation in critical Besov spaces ⋮ On the regularity of weak solutions for a modified dissipative quasi-geostrophic equation ⋮ Global well‐posedness of the aggregation equation with supercritical dissipation in Besov spaces ⋮ ON THE WELL-POSEDNESS OF A 2D NONLINEAR AND NONLOCAL SYSTEM ARISING FROM THE DISLOCATION DYNAMICS ⋮ Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum ⋮ Regularity results for a class of generalized surface quasi-geostrophic equations ⋮ On the Regularity Issues of a Class of Drift-Diffusion Equations with Nonlocal Diffusion ⋮ Decay of solutions to dissipative modified quasi-geostrophic equations ⋮ Hölder regularity in time of solutions to the generalized surface quasi-geostrophic equation

Cites Work

• Unnamed Item
• Unnamed Item
• Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
• Nonlocal maximum principles for active scalars
• Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Eventual regularization for the slightly supercritical quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• A maximum principle applied to quasi-geostrophic equations
• Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Variation on a theme of Caffarelli and Vasseur
• On the critical dissipative quasi-geostrophic equation
• Global regularity for a modified critical dissipative quasi-geostrophic equation
• Structure of the set of stationary solutions of the navier‐stokes equations
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces
• Behavior of Solutions of 2D Quasi-Geostrophic Equations

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