A direct approach to nonuniqueness and failure of compactness for the SQG equation

DOI10.1088/1361-6544/abe732zbMath1473.35580arXiv2007.03078OpenAlexW3162488300MaRDI QIDQ4994429

Philip Isett, Andrew Ma

Publication date: 18 June 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.03078

zbMATH Keywords

weak solutionsnonuniquenessh-principleOnsager conjectureSQGsurface quaisgeostrophic equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Meteorology and atmospheric physics (86A10) Weak solutions to PDEs (35D30) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations ⋮ Typicality results for weak solutions of the incompressible Navier–Stokes equations ⋮ Global solutions of a surface quasigeostrophic front equation ⋮ Onsager's conjecture for subgrid scale \(\alpha\)-models of turbulence ⋮ Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc ⋮ Energy conservation for the generalized surface quasi-geostrophic equation ⋮ A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity ⋮ Strong ill-posedness for SQG in critical Sobolev spaces ⋮ Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations ⋮ Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries

Cites Work

• On nonperiodic Euler flows with Hölder regularity
• Dissipative continuous Euler flows
• \(h\)-principles for the incompressible Euler equations
• Dissipative Euler flows and Onsager's conjecture
• Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
• Lack of uniqueness for weak solutions of the incompressible porous media equation
• Scaling exponents for active scalars
• Onsager's conjecture on the energy conservation for solutions of Euler's equation
• A proof of Onsager's conjecture
• Renormalization of active scalar equations
• Hölder continuous solutions of active scalar equations
• Convex integration and phenomenologies in turbulence
• Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces \(L^p\) or \(\dot{H}^{-1/2}\)
• \(C^1\) isometric imbeddings
• Holder Continuous Euler Flows in Three Dimensions with Compact Support in Time
• On Nash’s unique contribution to analysis in just three of his papers
• Onsager's Conjecture for Admissible Weak Solutions
• Uniqueness for SQG patch solutions
• Convex integration for a class of active scalar equations
• Surface quasi-geostrophic dynamics
• The ℎ-principle and the equations of fluid dynamics
• Nonuniqueness of Weak Solutions to the SQG Equation
• The Onsager theorem

This page was built for publication: A direct approach to nonuniqueness and failure of compactness for the SQG equation