Global well-posedness for a modified dissipative surface quasi-geostrophic equation in the critical Sobolev space \(H^{1}\)

DOI10.1016/j.jde.2010.09.021zbMath1210.35262OpenAlexW2031661410MaRDI QIDQ616474

Ramzi May

Publication date: 10 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.09.021

zbMATH Keywords

commutator estimatesChemin-Lerner's spacesmodified quasi-geostrophic equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (9)

Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation ⋮ Global regularity for the supercritical active scalars ⋮ Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ On the global regularity of two-dimensional generalized magnetohydrodynamics system ⋮ Long time behavior for the critical modified surface quasi-geostrophic equation ⋮ Global well-posedness for a modified critical dissipative quasi-geostrophic equation ⋮ Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces ⋮ Long time localization of modified surface quasi-geostrophic equations ⋮ Decay of solutions to dissipative modified quasi-geostrophic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space
• Uniqueness theorems for the three dimensional Navier-Stokes system
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• Existence and uniqueness results for the 2-D dissipative quasi-geostrophic equation
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• On the Navier-Stokes initial value problem. I
• On the critical dissipative quasi-geostrophic equation
• Density-dependent incompressible viscous fluids in critical spaces

This page was built for publication: Global well-posedness for a modified dissipative surface quasi-geostrophic equation in the critical Sobolev space \(H^{1}\)