Two remarks on generalized flows for ordinary differential equations.

DOI10.1016/j.crma.2007.05.010zbMath1132.34043OpenAlexW2006805805MaRDI QIDQ997968

Pierre-Louis Lions, Maxime Hauray, Claude Le Bris

Publication date: 10 August 2007

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

Full work available at URL: https://doi.org/10.1016/j.crma.2007.05.010

zbMATH Keywords

uniquenesslinear transport equationgeneralized flow solution

Mathematics Subject Classification ID

Linear differential equations in abstract spaces (34G10)

Related Items (8)

Critical non-Sobolev regularity for continuity equations with rough velocity fields ⋮ The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems ⋮ Differential equations with singular fields ⋮ A new proof of the uniqueness of the flow for ordinary differential equations with \(BV\) vector fields ⋮ Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients ⋮ Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms ⋮ Transport equation: extension of classical results for \(\operatorname{div}b\in\mathrm{BMO}\) ⋮ Convergence of numerical approximations to non-linear continuity equations with rough force fields

Cites Work

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• Transport equation and Cauchy problem for BV vector fields
• Ordinary differential equations, transport theory and Sobolev spaces
• Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow
• Estimates and regularity results for the DiPerna-Lions flow
• Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients
• Sur les équations différentielles ordinaires et les équations de transport

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