Global smooth dynamics of a fully ionized plasma with long-range collisions

Abstract

The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range collision kernel of soft potentials, particularly including the classical Coulomb collision, provided that initial data is smooth enough and decays in velocity variable fast enough. As a byproduct, the convergence rates of solutions are also obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of this complex system such as dispersion of the macro component in ${\mathbb{R}}^3$, singularity of the long-range collisions and regularity-loss of the electromagnetic field.

31 pages

References in corpus (2)

• The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$
• Global solutions to the Vlasov-Poisson-Landau System

Cited by in corpus (1)

• Negative Sobolev Spaces and the Two-species Vlasov-Maxwell-Landau System in the Whole Space