Global existence and long time behavior of the Ellipsoidal-Statistical-Fokker-Planck model for diatomic gases

Lei Jing; Jiawei Sun

doi:10.3934/krm.2020013

Article Contents

2020, Volume 13, Issue 2: 373-400. Doi: 10.3934/krm.2020013

This issue Previous Article Diffusion and kinetic transport with very weak confinement Next Article Asymptotic behavior of a second-order swarm sphere model and its kinetic limit

Global existence and long time behavior of the Ellipsoidal-Statistical-Fokker-Planck model for diatomic gases

Lei Jing^1, , and
Jiawei Sun^2,

1.
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

^* Corresponding author: Lei Jing
^* Corresponding author: Lei Jing

Received: April 30, 2019

Revised: October 31, 2019

Published: January 2020

The research was supported by National Natural Science Foundation of China grants No. 11671384, 11871047, 11931010, 11671120 and by the key research project of the Academy for Multidisciplinary Studies, Capital Normal University.

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Abstract

We are concerned with the global existence and long time behavior of the solutions to the ES-FP model for diatomic gases proposed in [22]. The global existence of the solutions for this model near the global Maxwellian is established by nonlinear energy method based on the macro-micro decomposition. An algebraic convergence rate in time of the solutions to the equilibrium state is obtained by constructing the compensating function. Since the density distribution function $ F(t, x, v, I) $ also contains energy variable $ I $, we derive more general Poincaré inequality including variables $ v, I $ on $ \mathbb{R}^3\times \mathbb{R}^+ $ to establish the coercivity estimate of the linearized operator.

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Mathematics Subject Classification: Primary: 35A01 35B40 35Q84; Secondary: 82C40.

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