Local existence and uniqueness theory of the Vlasov-Maxwell system

DOI10.1016/0022-247X(87)90143-0zbMath0645.35013MaRDI QIDQ1103096

Stephen Wollmann

Publication date: 1987

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenesssemigroup theorylinear transport equationsVlasov-Maxwell equationslinear symmetric hyperbolic equations

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Transport processes in time-dependent statistical mechanics (82C70) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items

On propagation of higher space regularity for nonlinear Vlasov equations, Local existence of solutions of the vlasov‐maxwell equations and convergence to the vlasov‐poisson equations for infinite light velocity, Solving the Vlasov-Maxwell equations using Hamiltonian splitting, Viscosity solutions for the Vlasov equation in the presence of a Yang-Mills field in temporal gauge, Viscosity solutions for the one-body Liouville equation in Yang-Mills charged Bianchi models with non-zero mass, Optimal control problem and viscosity solutions for the Vlasov equation in Yang-Mills charged Bianchi models, On the controllability of the relativistic Vlasov-Maxwell system, Nonlinear Instability of Vlasov--Maxwell Systems in the Classical and Quasineutral Limits, The conformal Einstein field equations with massless Vlasov matter

Cites Work

• Unnamed Item
• Singularity formation in a collisionless plasma could occur only at high velocities
• On local solutions of the initial value problem for the Vlasov-Maxwell equation
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• An existence and uniqueness theorem for the Vlasov-Maxwell system
• The use of the heat operator in an existence theory problem of the Vlasov equation
• Local existence of solutions of the vlasov‐maxwell equations and convergence to the vlasov‐poisson equations for infinite light velocity