Typicality results for weak solutions of the incompressible Navier–Stokes equations

DOI10.1051/cocv/2022038zbMath1492.35181arXiv2102.03244OpenAlexW3126888923WikidataQ114011448 ScholiaQ114011448MaRDI QIDQ5084463

Maria Colombo, Luigi De Rosa, Massimo Sorella

Publication date: 24 June 2022

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.03244

zbMATH Keywords

incompressible Navier-Stokes equationsBaire categoryconvex integrationLeray solutionsnonsmooth distributional solutions

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Classification of real functions; Baire classification of sets and functions (26A21)

Related Items

Sharp nonuniqueness for the Navier-Stokes equations ⋮ Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space ⋮ Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields

Cites Work

• Dissipative continuous Euler flows
• Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
• Non-uniqueness for the transport equation with Sobolev vector fields
• The Euler equations as a differential inclusion
• 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
• Positive solutions of transport equations and classical nonuniqueness of characteristic curves
• Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations
• Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations
• Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
• Convex integration and phenomenologies in turbulence
• Convex integration solutions to the transport equation with full dimensional concentration
• Non-renormalized solutions to the continuity equation
• The \(h\)-principle and Onsager's conjecture
• High dimensionality and h-principle in PDE
• Onsager's Conjecture for Admissible Weak Solutions
• The Navier-Stokes Problem in the 21st Century
• A direct approach to nonuniqueness and failure of compactness for the SQG equation
• Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces
• Nonuniqueness of Weak Solutions to the SQG Equation
• Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations

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