A Note on Two-Dimensional Transport with Bounded Divergence

DOI10.1080/03605300500455933zbMath1122.35143OpenAlexW1963704340MaRDI QIDQ5491387

Gianluca Crippa, Jeffrey Rauch, Ferruccio Colombini

Publication date: 11 October 2006

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500455933

zbMATH Keywords

transport equationdivergence-free vector fieldsrenormalized solutions

Mathematics Subject Classification ID

PDEs with low regular coefficients and/or low regular data (35R05) Transport processes in time-dependent statistical mechanics (82C70) Initial value problems for linear first-order PDEs (35F10)

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Cites Work

• Transport equation and Cauchy problem for BV vector fields
• Traces and fine properties of a \(BD\) class of vector fields and applications
• Ordinary differential equations, transport theory and Sobolev spaces
• On vector fields as generators of flows: A counterexample to Nelson's conjecture
• On two-dimensional Hamiltonian transport equations with \(\mathbb L^p_{\text{loc}}\) coefficients
• Uniqueness in the Cauchy problem for transport in \(\mathbb R^2\) and \(\mathbb R^{1+2}\)