On Liouville Transport Equation with Force Field inBVloc

DOI10.1081/PDE-120028850zbMath1103.35003arXiv1310.0976OpenAlexW1996105614MaRDI QIDQ3157890

Maxime Hauray

Publication date: 20 January 2005

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

Full work available at URL: https://arxiv.org/abs/1310.0976

Mathematics Subject Classification ID

Related Items (12)

The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems ⋮ A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics ⋮ Global existence of weak solutions for compressible Navier-Stokes equations: thermodynamically unstable pressure and anisotropic viscous stress tensor ⋮ Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications ⋮ Differential equations with singular fields ⋮ Propagation of 1D waves in regular discrete heterogeneous media: a Wigner measure approach ⋮ Free transport limit for \(N\)-particles dynamics with singular and short range potential ⋮ Well Posedness in any Dimension for Hamiltonian Flows with NonBVForce Terms ⋮ Stability of flows associated to gradient vector fields and convergence of iterated transport maps ⋮ Onsager-type conjecture and renormalized solutions for the relativistic Vlasov–Maxwell system ⋮ A review of the mean field limits for Vlasov equations ⋮ Diperna-Lions flow for relativistic particles in an electromagnetic field

Cites Work

• Ordinary differential equations, transport theory and Sobolev spaces
• On two-dimensional Hamiltonian transport equations with \(\mathbb L^p_{\text{loc}}\) coefficients
• Renormalized solutions to the Vlasov equation with coefficients of bounded variation

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