The non-cutoff Vlasov-Maxwell-Boltzmann system with weak angular singularity

DOI10.1007/s11425-016-9083-xzbMath1382.35007OpenAlexW2762647011MaRDI QIDQ1705566

Shuangqian Liu, Huijiang Zhao, Yingzhe Fan, Yuanjie Lei

Publication date: 16 March 2018

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-016-9083-x

zbMATH Keywords

time-velocity weighted energy methodglobal solutions near Maxwelliansnon-cutoff Vlasov-Maxwell-Boltzmann systemweak angular singularity

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Vlasov equations (35Q83)

Related Items (8)

From Vlasov-Maxwell-Boltzmann system to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law: convergence for classical solutions ⋮ Low regularity solutions for the Vlasov–Poisson–Landau/Boltzmann system ⋮ Hydrodynamic limit of the incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law from the Vlasov-Maxwell-Boltzmann system: Hilbert expansion approach ⋮ The Landau and non-cutoff Boltzmann equations in union of cubes ⋮ An \(\boldsymbol{L^1_{k}\cap L^{p}_{k}}\) Approach for the Non-Cutoff Boltzmann Equation in \(\boldsymbol{\mathbb{R}^3}\) ⋮ The Vlasov-Maxwell-Boltzmann system near Maxwellians with strong background magnetic field ⋮ Global solutions to the Vlasov-Poisson-Boltzmann system with weak angular singularity ⋮ The Vlasov-Maxwell-Landau system with Coulomb potential and strong background magnetic field

Cites Work

• The Vlasov-Poisson-Boltzmann system for the whole range of cutoff soft potentials
• The Vlasov-Poisson-Boltzmann system without angular cutoff
• Global smooth dynamics of a fully ionized plasma with long-range collisions
• Negative Sobolev spaces and the two-species Vlasov-Maxwell-Landau system in the whole space
• The Vlasov-Maxwell-Boltzmann system near Maxwellians in the whole space with very soft potentials
• Energy method for Boltzmann equation
• Optimal convergence rates of classical solutions for Vlasov-Poisson-Boltzmann system
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• Optimal time decay of the Vlasov-Poisson-Boltzmann system in \({\mathbb R^3}\)
• The Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions
• Cauchy problem for the Vlasov-Poisson-Boltzmann system
• The two-species Vlasov-Maxwell-Landau system in \(\mathbb{R}^3\)
• Global solutions and time decay of the non-cutoff Vlasov-Maxwell-Boltzmann system in the whole space
• The Vlasov-Maxwell-Boltzmann system in the whole space
• Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• The Landau equation in a periodic box
• Optimal time decay of the non cut-off Boltzmann equation in the whole space
• Decay of the two-species Vlasov-Poisson-Boltzmann system
• Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials
• 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
• Global classical solutions of the Boltzmann equation without angular cut-off
• Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space
• 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 $\mathbb{R}^3$
• Asymptotic Theory of the Boltzmann Equation

This page was built for publication: The non-cutoff Vlasov-Maxwell-Boltzmann system with weak angular singularity