Divergence-free vector fields in \(\mathbb R^2\)

DOI10.1007/s10958-010-0085-9zbMath1304.35214OpenAlexW1985674000MaRDI QIDQ461776

Stefano Bianchini, Gianluca Crippa, Giovanni Alberti

Publication date: 13 October 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-010-0085-9

zbMATH Keywords

transport equation

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 (2)

\(W^{1,p}\)-solutions of the transport equation by stochastic perturbation ⋮ Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition

Cites Work

• Transport equation and Cauchy problem for BV vector fields
• 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
• Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
• Uniqueness in the Cauchy problem for transport in \(\mathbb R^2\) and \(\mathbb R^{1+2}\)
• On two-dimensional Hamiltonian transport equations with continuous coefficients
• Estimates and regularity results for the DiPerna-Lions flow
• Weakly Differentiable Functions
• A Note on Two-Dimensional Transport with Bounded Divergence
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