Uniqueness in the Cauchy problem for transport in \(\mathbb R^2\) and \(\mathbb R^{1+2}\)

DOI10.1016/j.jde.2004.06.007zbMath1134.35311OpenAlexW2011293209MaRDI QIDQ1772320

Ferruccio Colombini, Jeffrey Rauch

Publication date: 18 April 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.06.007

zbMATH Keywords

Transport equationArea preservingUniqueness in the Cauchy problem

Mathematics Subject Classification ID

Related Items (9)

Critical non-Sobolev regularity for continuity equations with rough velocity fields ⋮ Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor ⋮ Markovian solutions to discontinuous ODEs ⋮ A uniqueness result for the continuity equation in two dimensions ⋮ Divergence-free vector fields in \(\mathbb R^2\) ⋮ Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms ⋮ A Note on Two-Dimensional Transport with Bounded Divergence ⋮ Convergence of numerical approximations to non-linear continuity equations with rough force fields ⋮ Diperna-Lions flow for relativistic particles in an electromagnetic field

Cites Work

• Ordinary differential equations, transport theory and Sobolev spaces
• On vector fields as generators of flows: A counterexample to Nelson's conjecture
• Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field
• Sur les équations différentielles ordinaires et les équations de transport
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