Convex integration solutions to the transport equation with full dimensional concentration
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Publication:2214922
DOI10.1016/j.anihpc.2020.03.002zbMath1458.35363arXiv1902.08521OpenAlexW2964429493MaRDI QIDQ2214922
Gabriel Sattig, Stefano Modena
Publication date: 10 December 2020
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.08521
Existence theories for optimal control problems involving partial differential equations (49J20) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Transport equations (35Q49)
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Cites Work
- 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
- Ordinary differential equations, transport theory and Sobolev spaces
- Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
- Elliptic partial differential equations of second order
- A proof of Onsager's conjecture
- Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications
- A quantitative theory for the continuity equation
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Non-renormalized solutions to the continuity equation
- Onsager's Conjecture for Admissible Weak Solutions
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