scholarly journals Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

2018 ◽  
Vol 170 (5) ◽  
pp. 895-931 ◽  
Author(s):  
Maxime Herda ◽  
L. Miguel Rodrigues
Keyword(s):  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Diffusive Limit ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

2012 ◽  
Vol 22 (11) ◽  
pp. 1250034 ◽  
Author(s):  
ANTON ARNOLD ◽  
IRENE M. GAMBA ◽  
MARIA PIA GUALDANI ◽  
STÉPHANE MISCHLER ◽  
CLEMENT MOUHOT ◽  
...  
Keyword(s):  
Steady State ◽  
Large Time ◽  
Planck Equation ◽  
Large Time Behavior ◽  
Positive Density ◽  
Time Behavior ◽  
Spectral Gaps ◽  
Harmonic Oscillator Potential ◽  
Fokker Planck Equation ◽  
Fokker Planck

We consider the linear Wigner–Fokker–Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker–Planck type operators in certain weighted L2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate.

Spectrum analysis of the linear Fokker–Planck equation

2017 ◽  
Vol 15 (03) ◽  
pp. 313-331 ◽  
Author(s):  
Lan Luo ◽  
Hongjun Yu
Keyword(s):  
Perturbation Theory ◽  
Linear Operator ◽  
Large Time ◽  
Semigroup Theory ◽  
Planck Equation ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Fokker Planck Equation ◽  
Spectrum Structure ◽  
Fokker Planck

In this work, we show the spectrum structure of the linear Fokker–Planck equation by using the semigroup theory and the linear operator perturbation theory. As an application, we show the large time behavior of the solutions to the linear Fokker–Planck equation.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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