Global existence and long time behavior of the ellipsoidal-statistical-Fokker-Planck model for diatomic gases
Global existence and long time behavior of the ellipsoidal-statistical-Fokker-Planck model for diatomic gases
复制标题
双原子气体椭球统计福克普朗克模型的全局存在性和长期行为
DOI：
10.3934/krm.2020013
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发表时间：
2020
影响因子：
1
通讯作者：
Jiawei Sun
中科院分区：
文献类型：
--
作者：
Lei Jing;Jiawei Sun
我们关注[22]中提出的双原子气体Es-FP模型解的整体存在性和长时间行为。利用基于宏微观分解的非线性能量方法，证明了该模型在全局麦克斯韦近似下解的整体存在性。通过构造补偿函数，得到了解在时间上的代数收敛速度。由于密度分布函数Begin{Document}$F(t，x，v，i)$\end{Document}也包含能量变量\Begin{Document}$i$\end{Document}，我们在Begin{Document}$\mathbb{R}^3\Times\mathbb{R}^+$\end{Document}上导出了包含变量\Begin{Document}$v，I$\end{Document}的更一般的Poincare不等式，从而建立了线性化算子的矫顽力估计。
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.