# American Institute of Mathematical Sciences

April  2020, 13(2): 373-400. doi: 10.3934/krm.2020013

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

 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

Received  May 2019 Revised  November 2019 Published  January 2020

Fund Project: 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.

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.

Citation: Lei Jing, Jiawei Sun. Global existence and long time behavior of the Ellipsoidal-Statistical-Fokker-Planck model for diatomic gases. Kinetic & Related Models, 2020, 13 (2) : 373-400. doi: 10.3934/krm.2020013
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