Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions
DOI10.2140/apde.2024.17.2161zbMATH Open1547.35592MaRDI QIDQ6596286
Alexey Cheskidov, Xiaoyutao Luo
Publication date: 2 September 2024
Published in: Analysis \& PDE (Search for Journal in Brave)
Smoothness and regularity of solutions to PDEs (35B65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Transport equations (35Q49)
Cites Work
- Unnamed Item
- Unnamed Item
- 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
- Non-uniqueness and prescribed energy for the continuity equation
- Ordinary differential equations, transport theory and Sobolev spaces
- The Euler equations as a differential inclusion
- On vector fields as generators of flows: A counterexample to Nelson's conjecture
- Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
- A proof of Onsager's conjecture
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Positive solutions of transport equations and classical nonuniqueness of characteristic curves
- Nonuniqueness of weak solutions for the transport equation at critical space regularity
- Anomalous dissipation in passive scalar transport
- Sharp nonuniqueness for the Navier-Stokes equations
- Convex integration solutions to the transport equation with full dimensional concentration
- Non-renormalized solutions to the continuity equation
- Mixing and un-mixing by incompressible flows
- Onsager's Conjecture for Admissible Weak Solutions
- Exponential self-similar mixing by incompressible flows
- A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation
- \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations
This page was built for publication: Extreme temporal intermittency in the linear Sobolev transport: almost smooth nonunique solutions
