Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations

DOI10.1137/19M1259900zbMath1439.35381arXiv1811.12870OpenAlexW2998947751WikidataQ126359626 ScholiaQ126359626MaRDI QIDQ5208285

Luigi De Rosa, Maria Colombo

Publication date: 15 January 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12870

zbMATH Keywords

time regularityEuler and Navier-Stokes equationsfractional dissipationHölder solutionsregularity of pressure

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Fractional derivatives and integrals (26A33) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11) Euler equations (35Q31)

Related Items (14)

Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations ⋮ Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations ⋮ A fractal version of the Onsager’s conjecture: The 𝛽-model ⋮ On double Hölder regularity of the hydrodynamic pressure in bounded domains ⋮ \(L^2\)-density of wild initial data for the hypodissipative Navier-Stokes equations ⋮ 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 \(\mathbb{T}^d\) ⋮ On the Helicity conservation for the incompressible Euler equations ⋮ On nonuniqueness of Hölder continuous globally dissipative Euler flows ⋮ Intermittency and lower dimensional dissipation in incompressible fluids ⋮ Regularity results for rough solutions of the incompressible Euler equations via interpolation methods ⋮ Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms ⋮ Hölder regularity in time of solutions to the generalized surface quasi-geostrophic equation ⋮ Hölder regularity of helicity for the incompressible flows

Cites Work

• Dissipative continuous Euler flows
• Dissipative Euler flows and Onsager's conjecture
• Onsager's conjecture on the energy conservation for solutions of Euler's equation
• Energy dissipation without viscosity in ideal hydrodynamics. I: Fourier analysis and local energy transfer
• A proof of Onsager's conjecture
• Ill-posedness of Leray solutions for the hypodissipative Navier-Stokes equations
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Anomalous dissipation for \(1/5\)-Hölder Euler flows
• Fractional Laplacian on the torus
• Dissipative Euler Flows with Onsager-Critical Spatial Regularity
• Local formulae for the hydrodynamic pressure and applications
• Parabolic Systems with Polynomial Growth and Regularity
• Onsager's Conjecture for Admissible Weak Solutions
• The existence of regular boundary points for non-linear elliptic systems
• Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations

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