Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space
From MaRDI portal
Publication:865076
DOI10.1007/s00220-006-0023-3zbMath1113.76029OpenAlexW2027849922MaRDI QIDQ865076
Publication date: 13 February 2007
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00220-006-0023-3
PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)
Related Items
Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation ⋮ A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation ⋮ Asymptotic study of supercritical surface quasi-geostrophic equation in critical space ⋮ Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift ⋮ Global well-posedness for a modified dissipative surface quasi-geostrophic equation in the critical Sobolev space \(H^{1}\) ⋮ On the global regularity of two-dimensional generalized magnetohydrodynamics system ⋮ Asymptotic behavior analysis for non-autonomous quasi-geostrophic equations in \(\mathbb{R}^2\) ⋮ Strong ill-posedness for SQG in critical Sobolev spaces ⋮ Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing ⋮ New numerical results for the surface quasi-geostrophic equation ⋮ Optimal Gevrey regularity for supercritical quasi-geostrophic equations ⋮ Long-time decay to the global solution of the 2D dissipative quasigeostrophic equation ⋮ Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation ⋮ Long time existence and asymptotic behavior of solutions for the 2D quasi-geostrophic equation with large dispersive forcing ⋮ Absence of anomalous dissipation of energy in forced two dimensional fluid equations ⋮ Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in \(\mathbb{R}^2\) ⋮ Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations ⋮ On the blow-up criterion for the quasi-geostrophic equations in homogeneous Besov spaces ⋮ On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces ⋮ Optimal estimates for far field asymptotics of solutions to the quasi-geostrophic equation ⋮ On Gevrey regularity of the supercritical SQG equation in critical Besov spaces ⋮ Remarks on the global regularity for the super-critical 2D dissipative quasi-geostrophic equation ⋮ On the quasi-geostrophic equations on compact closed surfaces in \(\mathbb{R}^3\) ⋮ Gevrey regularity for the supercritical quasi-geostrophic equation ⋮ Well-posedness for a transport equation with nonlocal velocity ⋮ Global well-posedness for Keller-Segel system in Besov type spaces ⋮ The well-posedness of the surface quasi-geostrophic equations in the Besov-Morrey spaces ⋮ Nonlinear instability for the critically dissipative quasi-geostrophic equation ⋮ Long time dynamics of forced critical SQG ⋮ Global smooth solutions to the \(n\)-dimensional damped models of incompressible fluid mechanics with small initial datum ⋮ 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 ⋮ Nonlinear instability for the surface quasi-geostrophic equation in the supercritical regime ⋮ Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations ⋮ A regularity criterion for the dissipative quasi-geostrophic equations ⋮ Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation ⋮ Global well‐posedness for the 2D dissipative quasi‐geostrophic equations in modulation spaces ⋮ Smoothing effect and well-posedness for 2D Boussinesq equations in critical Sobolev space ⋮ Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces ⋮ Asymptotic expansion of solutions to the nonlinear dissipative equation with the anomalous diffusion ⋮ Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries ⋮ Time periodic solutions to the 2D quasi-geostrophic equation with the supercritical dissipation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space
- Uniqueness theorems for the three dimensional Navier-Stokes system
- A maximum principle applied to quasi-geostrophic equations
- Global well-posedness in the super-critical dissipative quasi-geostrophic equations
- On the Navier-Stokes initial value problem. I
- On the critical dissipative quasi-geostrophic equation
- LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES
- Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data
- Behavior of Solutions of 2D Quasi-Geostrophic Equations
- On the two dimensional quasi-geostrophic equations
- Well-posedness for the Navier-Stokes equations
