On the one-dimensional continuity equation with a nearly incompressible vector field

DOI10.3934/cpaa.2019028zbMath1415.35085arXiv1610.08848OpenAlexW2964100249WikidataQ129036064 ScholiaQ129036064MaRDI QIDQ1633400

Y. Aharonov

Publication date: 20 December 2018

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.08848

zbMATH Keywords

non-smooth vector fieldlocally integrable weak solutions

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Hyperbolic conservation laws (35L65) Discontinuous ordinary differential equations (34A36) Weak solutions to PDEs (35D30) Initial value problems for linear first-order PDEs (35F10) Methods of ordinary differential equations applied to PDEs (35A24) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Uniqueness and Non-Uniqueness of Signed Measure-Valued Solutions to the Continuity Equation ⋮ Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension ⋮ Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

Cites Work

• On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation
• Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation
• Lagrangian flows and the one-dimensional Peano phenomenon for ODEs
• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• A system of non-strictly hyperbolic conservation laws arising in elasticity theory
• On the uniqueness of solutions to continuity equations
• A uniqueness result for the continuity equation in two dimensions
• An ill-posed Cauchy problem for a hyperbolic system in two space dimensions
• Renormalization for Autonomous Nearly Incompressible BV Vector Fields in Two Dimensions
• One-dimensional transport equations with discontinuous coefficients
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