Global smooth dynamics of a fully ionized plasma with long-range collisions
type: Item
instance of: scholarly article
title: Global smooth dynamics of a fully ionized plasma with long-range collisions
zbMATH Open document ID: 1305.82057
author: Renjun Duan
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2014-09-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1205.1635
review text: The author describes the dynamics of a fully ionized, two-component plasma under the influence of the self-consistent Lorentz force and binary collisions (taken into account by the Landau collision operator) by a system of kinetic transport equations and the Maxwell equations, which he calls ``Vlasov-Maxwell-Landau system''. The main aim of the paper is the prove the global existence of solutions of the Cauchy problem of the Vlasov-Maxwell-Landau system of equations in the form of a disturbed global Maxwellian velocity distribution under some conditions on the initial data. In doing so, the long-range collisional kernel of soft potentials, particularly including the classical Coulomb collisions, is taken into account -- assuming that both the Sobolev norm and the \(L^2_\xi(L^1_x)\)-norm of the initial perturbation ``with enough smoothness and enough velocity weight'' are sufficiently small. As a byproduct, also the convergence rates of the solutions are obtained. The proof is based on the energy method through designing a new temporal energy norm to capture different features of the complex system such as dispersion of the macro component in the velocity space, singularity of the long-range collisions and regularity-loss of the electromagnetic field.
reviewed by: Claudia-Veronika Meister
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 35Q84
Mathematics Subject Classification ID: 35Q83
zbMATH DE Number: 6349268
zbMATH Keywords: plasma physics
zbMATH Keywords: transport equations
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Landau kernel of soft potentials
zbMATH Keywords: global Maxwellian solution
zbMATH Keywords: disturbed Maxwell distribution function
MaRDI profile type: Publication
OpenAlex ID: W1978478716
arXiv ID: 1205.1635
cites work: On the Landau approximation in plasma physics.
cites work: Dispersion relations for the linearized Fokker-Planck equation
cites work: On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
cites work: GLOBAL SMOOTH FLOWS FOR THE COMPRESSIBLE EULER–MAXWELL SYSTEM: THE RELAXATION CASE
cites work: The Vlasov-Poisson-Boltzmann system in the whole space: The hard potential case
cites work: The Vlasov-Poisson-Boltzmann system for soft potentials
cites work: Optimal time decay of the Vlasov-Poisson-Boltzmann system in \({\mathbb R^3}\)
cites work: Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space
cites work: The Landau equation in a periodic box
cites work: The Vlasov-Poisson-Landau system in a periodic box
cites work: The Vlasov-Maxwell-Boltzmann system near Maxwellians
cites work: Q4429822
cites work: DECAY PROPERTY OF REGULARITY-LOSS TYPE AND APPLICATION TO SOME NONLINEAR HYPERBOLIC–ELLIPTIC SYSTEM
cites work: On the Cauchy problem of the Boltzmann and Landau equations with soft potentials
cites work: On Boltzmann and Landau equations
cites work: Boltzmann equation: micro-macro decompositions and positivity of shock profiles
cites work: The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation
cites work: Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators
cites work: Optimal time decay of the non cut-off Boltzmann equation in the whole space
cites work: Exponential decay for soft potentials near Maxwellian
cites work: Stability of the relativistic Maxwellian in a collisional plasma
cites work: On the existence of global solutions of mixed problem for non-linear Boltzmann equation
cites work: Q4409400
cites work: On the Cauchy problem for Landau equations: Sequential stability, global existence
cites work: Global classical solution of the Vlasov–Maxwell–Landau system near Maxwellians
cites work: Local existence of solutions to the Landau–Maxwell system
DOI: 10.1016/J.ANIHPC.2013.07.004
description: scientific article; zbMATH DE number 6349268