Negative Sobolev spaces and the two-species Vlasov-Maxwell-Landau system in the whole space

DOI10.1016/j.jfa.2014.09.011zbMath1304.35694arXiv1309.6388OpenAlexW2962816788MaRDI QIDQ461709

Huijiang Zhao, Yuanjie Lei

Publication date: 13 October 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.6388

zbMATH Keywords

global solutions near a given global Maxwelliannegative Sobolev spacestwo-species Vlasov-Maxwell-Landau system

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of plasmas (82D10) Vlasov equations (35Q83) Maxwell equations (35Q61) Boltzmann equations (35Q20)

Related Items (12)

The Vlasov-Poisson-Boltzmann system for the whole range of cutoff soft potentials ⋮ The relativistic Vlasov–Maxwell–Fokker–Planck system in the whole space ⋮ The Vlasov-Maxwell-Boltzmann system near Maxwellians with strong background magnetic field ⋮ Global solutions and time decay of the non-cutoff Vlasov-Maxwell-Boltzmann system in the whole space ⋮ The non-cutoff Vlasov-Maxwell-Boltzmann system with weak angular singularity ⋮ Global solutions to the Vlasov-Poisson-Boltzmann system with weak angular singularity ⋮ Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system ⋮ The Vlasov-Maxwell-Boltzmann system near Maxwellians in the whole space with very soft potentials ⋮ Unnamed Item ⋮ The Vlasov-Poisson-Landau system near a local Maxwellian ⋮ The Vlasov-Maxwell-Landau system with Coulomb potential and strong background magnetic field ⋮ Large-time behavior of the two-species relativistic Landau-Maxwell system in \(\mathbb{R}_x^3\)

Cites Work

• Unnamed Item
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• The Vlasov-Poisson-Boltzmann system in the whole space: The hard potential case
• Global smooth dynamics of a fully ionized plasma with long-range collisions
• Energy method for Boltzmann equation
• Optimal time decay of the Vlasov-Poisson-Boltzmann system in \({\mathbb R^3}\)
• Stability of the relativistic Maxwellian in a collisional plasma
• The Vlasov-Maxwell-Boltzmann system in the whole space
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• The Landau equation in a periodic box
• Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials
• The Boltzmann equation, Besov spaces, and optimal time decay rates in \(\mathbb{R}_x^n\)
• Exponential decay for soft potentials near Maxwellian
• The Vlasov-Poisson-Landau system in \(\mathbb{R}^{3}_{x}\)
• THE VLASOV–POISSON–BOLTZMANN SYSTEM FOR SOFT POTENTIALS
• The Vlasov-Poisson-Landau system in a periodic box
• Stability of the One-Species Vlasov–Poisson–Boltzmann System
• Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space
• Dissipative Property of the Vlasov–Maxwell–Boltzmann System with a Uniform Ionic Background
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND APPLICATION TO SOME NONLINEAR HYPERBOLIC–ELLIPTIC SYSTEM
• On Boltzmann and Landau equations
• Local existence of solutions to the Landau–Maxwell system
• Local existence of classical solutions to the Landau equations
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• The Boltzmann equation in the whole space
• Decay of Dissipative Equations and Negative Sobolev Spaces
• Global Solution and Time Decay of the Vlasov--Poisson--Landau System in $\mathbb{R}^3$
• On the Cauchy problem of the Boltzmann and Landau equations with soft potentials

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