Logarithmically regularized inviscid models in borderline sobolev spaces

DOI10.1063/1.4725531zbMath1329.76027OpenAlexW1987405226MaRDI QIDQ2872390

Jiahong Wu, Donghao Chae

Publication date: 14 January 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1fd5d9356ad33901a46f52a19b24470744ca1099

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Vortex flows for incompressible inviscid fluids (76B47) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (11)

Non existence and strong ill-posedness in \(C^k\) and Sobolev spaces for SQG ⋮ Long-time asymptotic behavior of the generalized two-dimensional quasi-geostrophic equation ⋮ Strong ill-posedness for SQG in critical Sobolev spaces ⋮ Strong ill-posedness of logarithmically regularized 2D Euler equations in the borderline Sobolev space ⋮ On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces ⋮ Global regularity of the axisymmetric Navier-Stokes model with logarithmically supercritical dissipation ⋮ Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces ⋮ On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces ⋮ On the local existence for an active scalar equation ⋮ Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces ⋮ Global \(\dot H^1 \cap \dot H^{-1}\) solutions to a logarithmically regularized \(2D\) Euler equation

Cites Work

• Unnamed Item
• Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
• Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations
• Theory of function spaces
• A maximum principle applied to quasi-geostrophic equations
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Surface quasi-geostrophic dynamics
• Non-stationary flow of an ideal incompressible liquid
• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations

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