Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
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Publication:1626418
DOI10.1016/j.jfa.2018.10.001zbMath1402.35008arXiv1701.04603OpenAlexW2963980879MaRDI QIDQ1626418
Albert Clop, Heikki Jylhä, Joan Orobitg, Joan Mateu
Publication date: 27 November 2018
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.04603
Hyperbolic conservation laws (35L65) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Related Items (9)
Uniqueness and Non-Uniqueness of Signed Measure-Valued Solutions to the Continuity Equation ⋮ Classical flows of vector fields with exponential or sub-exponential summability ⋮ Existence and uniqueness for the transport of currents by Lipschitz vector fields ⋮ Discontinuous nonlocal conservation laws and related discontinuous ODEs -- existence, uniqueness, stability and regularity ⋮ The transport equation in the scaling invariant Besov or Essén-Janson-Peng-Xiao space ⋮ A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation ⋮ FLOW WITH DENSITY AND TRANSPORT EQUATION IN ⋮ Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations
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