Global weak solutions of Vlasov‐Maxwell systems

1989/09/01 by R. J. Diperna, Ronald J. DiPerna, P. L. Lions +1 · 16 citations
Mathematics · #Gas Dynamics and Kinetic Theory #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions

paper · doi:10.1002/cpa.3160420603

Abstract

Abstract We study here the Vlasov‐Maxwell system in its classical and relativistic form. We prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data. The main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work.

Citations

• Absence of shocks in an initially dilute collisionless plasma
• Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data
• Singularity formation in a collisionless plasma could occur only at high velocities

Cited by

• Hilbert’s 6th problem: the relativistic version
• Microscopic Foundations of Kinetic Plasma Theory: The Relativistic Vlasov–Maxwell Equations and Their Radiation-Reaction-Corrected Generalization
• A particle approximation for the relativistic Vlasov-Maxwell dynamics
• Velocity Averaging Lemmas: Classical, Quantum and Semi-Classical
• Solutions of the Vlasov-Maxwell-Boltzmann system with long-range\n interactions
• Critical velocity averaging lemmas
• Global Classical Solutions to the Relativistic Boltzmann Equation\n without Angular Cut-off
• Vlasov equation coupled with non-Newtonian fluids with discontinuous-in-time stress tensor
• Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
• Stability analysis of collisionless plasmas with specularly reflecting\n boundary
• Averaging lemmas with a force term in the transport equation
• Well-posedness of Weak and Strong Solutions to the Kinetic Cucker-Smale Model
• On the weak flocking of the kinetic Cucker-Smale model in a fully non-compact support setting
• An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws
• The Einstein-Vlasov System/Kinetic Theory. [europepmc]
• The Einstein-Vlasov System/Kinetic Theory. [europepmc]

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