Global weak solutions to the relativistic Vlasov-Maxwell system revisited
Gerhard Rein
TL;DR
This paper revisits the existence of global weak solutions to the relativistic Vlasov-Maxwell system, providing a simplified proof to make the foundational result more accessible to newcomers.
Contribution
It offers a simplified proof of the existence of global weak solutions for the relativistic Vlasov-Maxwell system, enhancing understanding in kinetic theory.
Findings
Weak solutions preserve total charge
Simplified proof increases accessibility
Confirms global existence in relativistic case
Abstract
In 1989, R. DiPerna and P.-L. Lions established the existence of global weak solutions to the Vlasov-Maxwell system. In the present notes we give a somewhat simplified proof of this result for the relativistic version of this system, the main purpose being to make this important result of kinetic theory more easily accessible to newcomers in the field. We show that the weak solutions preserve the total charge.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Computational Fluid Dynamics and Aerodynamics · Laser-Plasma Interactions and Diagnostics