Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation

DOI10.1016/j.jde.2012.04.003zbMath1308.76065OpenAlexW1993734945MaRDI QIDQ432455

Liutang Xue, Xiaoxin Zheng

Publication date: 4 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.04.003

zbMATH Keywords

modulus of continuitysurface quasi-geostrophic equationnonlocal maximum principleslightly supercritical equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Meteorology and atmospheric physics (86A10) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) PDEs in connection with geophysics (35Q86)

Related Items (11)

Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ Weak-strong uniqueness criterion for the \(\beta\)-generalized surface quasi-geostrophic equation ⋮ Energy conservation for the generalized surface quasi-geostrophic equation ⋮ On the Serrin's regularity criterion for the \(\beta\)-generalized dissipative surface quasi-geostrophic equation ⋮ On the viscous instabilities and transitions of two-layer model with a layered topography ⋮ Absence of anomalous dissipation of energy in forced two dimensional fluid equations ⋮ Note on the weak-strong uniqueness criterion for the \(\beta\)-QG in Morrey-Campanato space ⋮ Nonlocal nonlinear advection-diffusion equations ⋮ Long time dynamics of forced critical SQG ⋮ Regularity results for a class of generalized surface quasi-geostrophic equations ⋮ Nonlinear instability for the surface quasi-geostrophic equation in the supercritical regime

Cites Work

• Nonlocal maximum principles for active scalars
• Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
• On the regularity of a class of generalized quasi-geostrophic equations
• Global well-posedness for a modified critical dissipative quasi-geostrophic equation
• Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Nonlinear maximum principles for dissipative linear nonlocal operators and applications
• Variation on a theme of Caffarelli and Vasseur
• Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation
• Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
• The magneto-geostrophic equations: a survey
• Fourier Analysis and Nonlinear Partial Differential Equations
• Incompressible flow in porous media with fractional diffusion
• Global regularity for a modified critical dissipative quasi-geostrophic equation
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Behavior of Solutions of 2D Quasi-Geostrophic Equations

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