Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation

DOI10.1016/j.crma.2016.10.009zbMath1430.35050arXiv1608.04324OpenAlexW2963361680MaRDI QIDQ344326

Laura Caravenna, Gianluca Crippa

Publication date: 22 November 2016

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04324

Mathematics Subject Classification ID

Initial value problems for linear first-order PDEs (35F10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

On the one-dimensional continuity equation with a nearly incompressible vector field ⋮ Convex integration solutions to the transport equation with full dimensional concentration ⋮ Non-uniqueness for the transport equation with Sobolev vector fields ⋮ A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation ⋮ Sobolev estimates for solutions of the transport equation and ODE flows associated to non-Lipschitz drifts ⋮ Nonuniqueness of weak solutions for the transport equation at critical space regularity ⋮ Regularization by noise in one-dimensional continuity equation ⋮ Non-renormalized solutions to the continuity equation

Cites Work

• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• The disintegration of the Lebesgue measure on the faces of a convex function
• Estimates and regularity results for the DiPerna-Lions flow

This page was built for publication: Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation