Non-existence and strong ill-posedness in \(C^{k, \beta}\) for the generalized surface quasi-geostrophic equation

DOI10.1007/S00220-024-05049-9zbMATH Open1543.35244MaRDI QIDQ6568765

Luis Martínez-Zoroa, Diego Córdoba

Publication date: 8 July 2024

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

zbMATH Keywords

rotationsill-posednessquasi-geostrophic equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Ill-posed problems for PDEs (35R25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with geophysics (35Q86) Geophysical flows (76U60)

Cites Work

• Inviscid models generalizing the two-dimensional Euler and the surface quasi-geostrophic equations
• Ill-posedness for the incompressible Euler equations in critical Sobolev spaces
• Uniformly rotating smooth solutions for the incompressible 2D Euler equations
• On Kato-Ponce and fractional Leibniz
• Small-scale creation for solutions of the SQG equation
• On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces
• Non existence and strong ill-posedness in \(C^k\) and Sobolev spaces for SQG
• Strong ill-posedness of logarithmically regularized 2D Euler equations in the borderline Sobolev space
• \(L^\infty\) ill-posedness for a class of equations arising in hydrodynamics
• Strong illposedness of the incompressible Euler equation in integer \(C^m\) spaces
• Solutions of the 2D quasi-geostrophic equation in Hölder spaces
• Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces
• On the ill-posedness of active scalar equations with odd singular kernels
• Logarithmically regularized inviscid models in borderline sobolev spaces
• Generalized surface quasi-geostrophic equations with singular velocities
• A Simple Energy Pump for the Surface Quasi-geostrophic Equation
• Global Smooth Solutions for the Inviscid SQG Equation
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation
• Nonuniqueness of Weak Solutions to the SQG Equation
• Smooth Travelling-Wave Solutions to the Inviscid Surface Quasi-Geostrophic Equation
• Existence of solutions to fluid equations in Hölder and uniformly local Sobolev spaces
• Strong ill-posedness for SQG in critical Sobolev spaces

Related Items (3)

Global unique solutions with instantaneous loss of regularity for SQG with fractional diffusion ⋮ Existence of asymmetric vortex patch for the generalized SQG equations ⋮ Strong ill-Posedness in \(L^\infty\) of the 2D Boussinesq equations in vorticity form and application to the 3D axisymmetric Euler equations

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