Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

DOI10.1016/j.anihpc.2007.10.001zbMath1149.76052arXivmath/0701592OpenAlexW2060099728MaRDI QIDQ957581

Jiahong Wu, Peter Constantin

Publication date: 28 November 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701592

zbMATH Keywords

Leray-Hopf weak solutionsupercritical dissipation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) General theory of rotating fluids (76U05) Meteorology and atmospheric physics (86A10)

Related Items (73)

Regularity criterion and energy conservation for the supercritical quasi-geostrophic equation ⋮ Global well-posedness of slightly supercritical SQG equations and gradient estimate ⋮ Regularity for the supercritical fractional Laplacian with drift ⋮ Global regularity results of the 2D Boussinesq equations with fractional Laplacian dissipation ⋮ Non linear singular drifts and fractional operators: when Besov meets Morrey and Campanato ⋮ Formation of singularities for multi-dimensional transport equations with nonlocal velocity ⋮ Critical SQG in bounded domains ⋮ Global existence for the regularized surface quasi-geostrophic equation and its inviscid limits ⋮ A logarithmically improved regularity criterion for the supercritical quasi-geostrophic equations in Besov space ⋮ Global regularity for the supercritical active scalars ⋮ On the second iterate for critically diffusive active scalar equations ⋮ Local well-posedness for the quasi-geostrophic equations in Besov-Lorentz spaces ⋮ Global regularity for several incompressible fluid models with partial dissipation ⋮ On the differentiability issue of the drift-diffusion equation with nonlocal Lévy-type diffusion ⋮ Nonlinear maximum principles for dissipative linear nonlocal operators and applications ⋮ Long-time behavior of subcritical 2D vorticity Boussinesq equations ⋮ Blowup of solutions for a transport equation with nonlocal velocity and damping ⋮ A frequency localized maximum principle applied to the 2D quasi-geostrophic equation ⋮ Remarks on the method of modulus of continuity and the modified dissipative porous media equation ⋮ Global smoothness for a 1D supercritical transport model with nonlocal velocity ⋮ New numerical results for the surface quasi-geostrophic equation ⋮ On electroconvection in porous media ⋮ Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation ⋮ On the self-similar solutions of the 3D Euler and the related equations ⋮ Long-time behavior and critical limit of subcritical SQG equations in scale-invariant Sobolev spaces ⋮ Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation ⋮ The 2D regularized incompressible Boussinesq equations with general critical dissipations ⋮ Hölder estimates for fractional parabolic equations with critical divergence free drifts ⋮ On the regularity of a class of generalized quasi-geostrophic equations ⋮ Global in time classical solutions to the 3D quasi-geostrophic system for large initial data ⋮ On a 1D transport equation with nonlocal velocity and supercritical dissipation ⋮ Yudovich type solution for the 2D inviscid Boussinesq system with critical and supercritical dissipation ⋮ On the well-posedness of the quasi-geostrophic equation in the Triebel-Lizorkin-Lorentz spaces ⋮ Variation on a theme of Caffarelli and Vasseur ⋮ Absence of anomalous dissipation of energy in forced two dimensional fluid equations ⋮ Applications of harmonic analysis techniques to regularity problems of dissipative equations ⋮ A logarithmically improved regularity criterion for the surface quasi-geostrophic equation ⋮ Global and local existence for the dissipative critical SQG equation with small oscillations ⋮ Hölder regularity up to the boundary for critical SQG on bounded domains ⋮ On the regularity of weak solutions for a modified dissipative quasi-geostrophic equation ⋮ Remarks on the improved regularity criterion for the 2D Euler-Boussinesq equations with supercritical dissipation ⋮ Fractional operators with singular drift: smoothing properties and Morrey-Campanato spaces ⋮ Nonlocal nonlinear advection-diffusion equations ⋮ Gevrey regularity for the supercritical quasi-geostrophic equation ⋮ Regularity of Hölder continuous solutions of the supercritical porous media equation ⋮ Eventual regularization for the slightly supercritical quasi-geostrophic equation ⋮ The well-posedness of the surface quasi-geostrophic equations in the Besov-Morrey spaces ⋮ Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics ⋮ Long time dynamics of forced critical SQG ⋮ Nonlocal maximum principles for active scalars ⋮ Eventual regularity of the two-dimensional Boussinesq equations with supercritical dissipation ⋮ Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum ⋮ A molecular method applied to a non-local PDE in stratified Lie groups ⋮ Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations ⋮ On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces ⋮ Regularity results for a class of generalized surface quasi-geostrophic equations ⋮ On the Euler equations of incompressible fluids ⋮ Nonlinear instability for the surface quasi-geostrophic equation in the supercritical regime ⋮ A regularity criterion for the dissipative quasi-geostrophic equations ⋮ Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations ⋮ Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation ⋮ Higher regularity of Hölder continuous solutions of parabolic equations with singular drift velocities ⋮ The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces ⋮ Estimates near the boundary for critical SQG ⋮ Discontinuous Fronts as Exact Solutions to Precipitating Quasi-geostrophic Equations ⋮ On the Regularity Issues of a Class of Drift-Diffusion Equations with Nonlocal Diffusion ⋮ Commutator estimate and its application to regularity criteria of the dissipative quasi-geostrophic equation ⋮ Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms ⋮ A class of large solutions to the supercritical surface quasi-geostrophic equation ⋮ On the global regularity for the anisotropic dissipative surface quasi-geostrophic equation ⋮ Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces ⋮ Global well-posedness, regularity and blow-up for the \(\beta\)-CCF model ⋮ Hölder regularity in time of solutions to the generalized surface quasi-geostrophic equation

Cites Work

• Unnamed Item
• Global solutions to the two-dimensional quasi-geostrophic equation with critical or super-critical dissipation
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A maximum principle applied to quasi-geostrophic equations
• Global well-posedness in the super-critical dissipative quasi-geostrophic equations
• Existence and uniqueness results for the 2-D dissipative quasi-geostrophic equation
• 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
• Solutions of the 2D quasi-geostrophic equation in Hölder spaces
• The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations
• Non-radial self-similar solutions for the critical dissipative quasi-geostrophic equation.
• Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows
• On the critical dissipative quasi-geostrophic equation
• THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONS
• Euler Equations, Navier-Stokes Equations and Turbulence
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Asymptotic Behavior to Dissipative Quasi-Geostrophic Flows
• Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces
• The two-dimensional quasi-geostrophic equation with critical or supercritical dissipation
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Surface quasi-geostrophic dynamics
• On the Regularity Conditions for the Dissipative Quasi-geostrophic Equations

This page was built for publication: Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation