Non-renormalized solutions to the continuity equation
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Publication:2338496
DOI10.1007/s00526-019-1651-8zbMath1428.35005arXiv1806.09145OpenAlexW2986053180WikidataQ114229052 ScholiaQ114229052MaRDI QIDQ2338496
László jun. Székelyhidi, Stefano Modena
Publication date: 21 November 2019
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.09145
Initial value problems for linear first-order PDEs (35F10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
- Unnamed Item
- On nonperiodic Euler flows with Hölder regularity
- Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation
- Non-uniqueness and \(h\)-principle for Hölder-continuous weak solutions of the Euler equations
- Non-uniqueness for the transport equation with Sobolev vector fields
- Transport equation and Cauchy problem for BV vector fields
- On admissibility criteria for weak solutions of the Euler equations
- Ordinary differential equations, transport theory and Sobolev spaces
- Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
- A proof of Onsager's conjecture
- Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Convex integration solutions to the transport equation with full dimensional concentration
- A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\)
- Anomalous dissipation for \(1/5\)-Hölder Euler flows
- Onsager's Conjecture for Admissible Weak Solutions
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