Nonresonant smoothing for coupled wave and transport equations and the Vlasov-Maxwell system

DOI10.4171/RMI/409zbMath1064.35097MaRDI QIDQ1772121

Christophe Pallard, François Golse, François Bouchut

Publication date: 15 April 2005

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1098885437

zbMATH Keywords

propagation speed

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Wave equation (35L05) Nonlinear first-order PDEs (35F20) PDEs in connection with relativity and gravitational theory (35Q75) Statistical mechanics of plasmas (82D10) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (12)

Mean field limit for particles interacting with a vibrating medium ⋮ The energy conservation for weak solutions to the relativistic Nordström-Vlasov system ⋮ The mean-field limit for a regularized Vlasov-Maxwell dynamics ⋮ Microscopic foundations of kinetic plasma theory: the relativistic Vlasov-Maxwell equations and their radiation-reaction-corrected generalization ⋮ Energy conservation of the DiPerna-Lions solutions to Vlasov-Maxwell systems ⋮ Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system ⋮ Nonresonant smoothing in Sobolev spaces for coupled wave + transport equations. ⋮ On global smooth solutions to the 3D Vlasov-Nordström system ⋮ The Vlasov limit for a system of particles which interact with a wave field ⋮ Onsager-type conjecture and renormalized solutions for the relativistic Vlasov–Maxwell system ⋮ Particles Interacting with a Vibrating Medium: Existence of Solutions and Convergence to the Vlasov--Poisson System ⋮ Regularity of weak solutions for the relativistic Vlasov–Maxwell system

Cites Work

• Singularity formation in a collisionless plasma could occur only at high velocities
• Absence of shocks in an initially dilute collisionless plasma
• Regularity of the moments of the solution of a transport equation
• A new approach to study the Vlasov-Maxwell system.
• Finite energy solutions of the Yang-Mills equations in \(\mathbb{R}^{3+1}\)
• A perturbative analysis of the time-envelope approximation in strong Langmuir turbulence
• \(H^p\) spaces of several variables
• Global weak solutions of Vlasov‐Maxwell systems
• High velocity particles in a collisionless plasma
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