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

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 \begin{document}$ F(t, x, v, I) $\end{document} also contains energy variable \begin{document}$ I $\end{document} , we derive more general Poincare inequality including variables \begin{document}$ v, I $\end{document} on \begin{document}$ \mathbb{R}^3\times \mathbb{R}^+ $\end{document} to establish the coercivity estimate of the linearized operator.