Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

DOI10.4171/JEMS/1162zbMath1493.35063arXiv1809.00600OpenAlexW3209887221MaRDI QIDQ2143210

Maria Colombo, Tristan Buckmaster, Vlad C. Vicol

Publication date: 31 May 2022

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.00600

zbMATH Keywords

Navier-Stokes equationspartial regularitynon-uniquenessconvex integrationwild solutions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractals (28A80) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dissipative continuous Euler flows
• Dissipative Euler flows and Onsager's conjecture
• Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
• Non-uniqueness for the transport equation with Sobolev vector fields
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
• Partial regularity of solutions to the Navier-Stokes equations
• A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation
• 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
• Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent
• Partial regularity of suitable weak solutions to the fractional Navier-Stokes equations
• Non-renormalized solutions to the continuity equation
• Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?
• Anomalous dissipation for \(1/5\)-Hölder Euler flows
• On the Navier-Stokes initial value problem. I
• Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
• Onsager's conjecture almost everywhere in time
• Un teorema di unicita per le equazioni di Navier-Stokes
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• UNIQUENESS OF MILD SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN LN
• Dissipative Euler Flows with Onsager-Critical Spatial Regularity
• Onsager's Conjecture for Admissible Weak Solutions
• The Three-Dimensional Navier–Stokes Equations
• The Navier-Stokes Problem in the 21st Century
• The fractal dimension of the singular set for solutions of the Navier–Stokes system
• Partial regularity of suitable weak solutions of the navier-stokes equations
• The Generalized Caffarelli‐Kohn‐Nirenberg Theorem for the Hyperdissipative Navier‐Stokes System
• Decay of weak solutions and the singular set of the three-dimensional Navier–Stokes equations
• Quelques résultats d'existence dans des équations aux dérivées partielles non linéaires
• Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations
• Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
• Well-posedness for the Navier-Stokes equations
• Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces

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