Smoothing does not give a selection principle for transport equations with bounded autonomous fields
DOI10.1007/s40316-021-00160-yzbMath1491.35381arXiv2011.12093OpenAlexW3135842998MaRDI QIDQ2118369
Camillo De Lellis, Vikram Giri
Publication date: 22 March 2022
Published in: Annales Mathématiques du Québec (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.12093
Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Weak solutions to PDEs (35D30) Initial value problems for first-order hyperbolic equations (35L03) Transport equations (35Q49)
Related Items (2)
Cites Work
- Existence and uniqueness of maximal regular flows for non-smooth vector fields
- 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
- On vector fields as generators of flows: A counterexample to Nelson's conjecture
- Singular integrals and a problem on mixing flows
- Positive solutions of transport equations and classical nonuniqueness of characteristic curves
- Smooth approximation is not a selection principle for the transport equation with rough vector field
- A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\)
- Mixing and un-mixing by incompressible flows
- A uniqueness result for the continuity equation in two dimensions
- On the commutativity of flows of rough vector fields
- Estimates and regularity results for the DiPerna-Lions flow
- Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms
- Exponential self-similar mixing by incompressible flows
- Structure of level sets and Sard-type properties of Lipschitz maps
- Unnamed Item
- Unnamed Item
This page was built for publication: Smoothing does not give a selection principle for transport equations with bounded autonomous fields
