Diffusion limit and the optimal convergence rate of the Vlasov-Poisson-Fokker-Planck system

DOI10.3934/krm.2021041zbMath1486.76117arXiv2208.03746OpenAlexW4205571666MaRDI QIDQ2122775

Ming-ying Zhong

Publication date: 7 April 2022

Published in: Kinetic and Related Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.03746

zbMATH Keywords

spectral analysisoptimal convergence ratediffusion limitglobal Maxwelliandrift-diffusion Poisson systemrescaled Vlasov-Poisson-Fokker-Planck system

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Vlasov equations (35Q83) Fokker-Planck equations (35Q84)

Related Items

Diffusive Limit of the Vlasov–Poisson–Fokker–Planck Model: Quantitative and Strong Convergence Results

Cites Work

• Unnamed Item
• Unnamed Item
• Diffusion limit of the Vlasov-Poisson-Boltzmann system
• Diffusion limit of the Vlasov-Poisson-Fokker-Planck system
• Semigroups of linear operators and applications to partial differential equations
• On the existence of global weak solutions for Vlasov-Poisson-Fokker- Planck systems
• Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensions
• On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
• Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems
• Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
• Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system
• Quasi-hydrodynamic semiconductor equations
• The first and second fluid approximation to the linearized Boltzmann equation
• On the time-dependent drift-diffusion model for semiconductors
• Smoothing effect for the nonlinear Vlasov-Poisson-Fokker-Planck system
• On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
• Spectrum analysis for the Vlasov-Poisson-Boltzmann system
• Diffusion limit of kinetic equations for multiple species charged particles
• Multidimensional high-field limit of the electrostatic Vlasov-Poisson-Fokker-Planck system
• On large time asymptotics for drift-diffusion-poisson systems
• THE CLASSICAL INCOMPRESSIBLE NAVIER-STOKES LIMIT OF THE BOLTZMANN EQUATION
• A nonstationary problem in the theory of electrolytes
• Global weak solutions for the initial-boundary-value problems Vlasov-Poisson-Fokker-Planck System
• The Debye system: existence and large time behavior of solutions
• Asymptotic Behavior of an Initial-Boundary Value Problem for the Vlasov--Poisson--Fokker--Planck System
• Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions
• PARABOLIC LIMIT AND STABILITY OF THE VLASOV–FOKKER–PLANCK SYSTEM
• On the initial value problem for the Vlasov‐Poisson‐Fokker‐Planck system with initial data in L^p spaces
• Large time behavior of solutions to Vlasov-Poisson-Landau\\ (Fokker-Planck) equations
• Spectrum analysis of the linear Fokker–Planck equation
• HYDRODYNAMIC LIMIT FOR THE VLASOV–POISSON–FOKKER–PLANCK SYSTEM: ANALYSIS OF THE TWO-DIMENSIONAL CASE
• High-field limit for the Vlasov-Poisson-Fokker-Planck system.