Article ID Journal Published Year Pages File Type
4604260 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2014 28 Pages PDF
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 both the Sobolev norm and Lξ2(Lx1)-norm of initial perturbation with enough smoothness and enough velocity weight is sufficiently small. 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 R3, singularity of the long-range collisions and regularity-loss of the electromagnetic field.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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