Well-posedness and trend to equilibrium for the Vlasov-Poisson-Fokker-Planck system with a confining potential

DOI10.3934/KRM.2024011MaRDI QIDQ6657891

Publication date: 7 January 2025

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

Fokker-Planck equation semigroup mild solution convergence to equilibrium long time behavior kinetic theory of gases hypocoercivity Vlasov-Poisson equation hypoelliptic regularity Lypunov functional

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Vlasov equations (35Q83) Fokker-Planck equations (35Q84)

Cites Work

Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Title not available (Why is that?)
Statistical mechanics of gravitating systems
Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
Hypocoercivity for kinetic equations with linear relaxation terms
A simple proof of the Poincaré inequality for a large class of probability measures
Semigroups of linear operators and applications to partial differential equations
Interpolation of semigroups and integrated semigroups
On the existence of global weak solutions for Vlasov-Poisson-Fokker- Planck systems
The Boltzmann equation and its applications
Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (large time behavior and steady states)
On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equation
Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime
On multi-dimensional hypocoercive BGK models
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
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
Logarithmic Sobolev inequalities and stochastic Ising models
Regular solutions of the Vlasov-Poisson-Fokker-Planck system.
Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
Smoothing effect for the nonlinear Vlasov-Poisson-Fokker-Planck system
Steady states of the Vlasov-Poisson-Fokker-Planck system
On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
$H$-theorem for electrostatic or self-gravitating Vlasov-Poisson-Fokker-Planck systems.
$\mathrm{L}^2$-hypocoercivity and large time asymptotics of the linearized Vlasov-Poisson-Fokker-Planck system
Hypoelliptic second order differential equations
On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential
Invariant manifolds and long-time asymptotics for the Vlasov--Poisson--Fokker--Planck equation
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
Hypocoercivity
Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions
STATIONARY STATES IN PLASMA PHYSICS: MAXWELLIAN SOLUTIONS OF THE VLASOV-POISSON SYSTEM
Long-time behaviour for solutions of the Vlasov-Poisson-Fokker-Planck equation
The Vlasov‐Poisson‐Boltzmann system near Maxwellians
On the initial value problem for the Vlasov‐Poisson‐Fokker‐Planck system with initial data in L^p spaces
Analysis and Geometry of Markov Diffusion Operators
Hypocoercivity for linear kinetic equations conserving mass
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
Brownian Motion, Dynamical Friction, and Stellar Dynamics
Stochastic Problems in Physics and Astronomy
Global existence of regular solutions for the Vlasov-Poisson-Fokker-Planck system

This page was built for publication: Well-posedness and trend to equilibrium for the Vlasov-Poisson-Fokker-Planck system with a confining potential

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6657891)