Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations

DOI10.2140/apde.2022.15.405zbMath1490.35263arXiv1908.03529OpenAlexW3016426108MaRDI QIDQ2128851

Riccardo Tione, Luigi De Rosa

Publication date: 22 April 2022

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03529

zbMATH Keywords

incompressible Euler equationsBaire categoryconvex integrationHölder solutionsenergy regularity

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Classification of real functions; Baire classification of sets and functions (26A21) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Related Items

Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations ⋮ Regularity of almost-minimizers of Hölder-coefficient surface energies ⋮ Typicality results for weak solutions of the incompressible Navier–Stokes equations ⋮ Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space ⋮ On double Hölder regularity of the hydrodynamic pressure in bounded domains ⋮ Regularity in time along the coarse scale flow for the incompressible Euler equations ⋮ Onsager's energy conservation of solutions for density-dependent Euler equations in \(\mathbb{T}^d\) ⋮ Dissipation in Onsager's critical classes and energy conservation in \(BV \cap L^\infty\) with and without boundary ⋮ Intermittency and lower dimensional dissipation in incompressible fluids ⋮ Hölder regularity in time of solutions to the generalized surface quasi-geostrophic equation ⋮ Hölder regularity of helicity for the incompressible flows

Cites Work

• On nonperiodic Euler flows with Hölder regularity
• Dissipative continuous Euler flows
• On the kinetic energy profile of Hölder continuous Euler flows
• Onsager's conjecture on the energy conservation for solutions of Euler's equation
• A proof of Onsager's conjecture
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Onsager's Conjecture for Admissible Weak Solutions
• Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations

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