Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force
Cauchy problem on the Vlasov-Fokker-Planck equation coupled with the compressible Euler equations through the friction force
复制标题
DOI：
10.3934/krm.2013.6.687
复制
发表时间：
2013-11
影响因子：
1
通讯作者：
Renjun Duan;Shuangqiang Liu
中科院分区：
文献类型：
--
作者：
Renjun Duan;Shuangqiang Liu
我们所关心的两相流系统组成的Vlasov-Fokker-Planck方程的颗粒耦合到可压缩的欧拉方程的流体通过摩擦力。在扰动框架下建立了Cauchy问题的整体适定性，并在初值的一些附加条件下得到了解向平衡点的收敛速度，这些收敛速度在整个空间上是代数的，在环面上是指数的.证明是基于经典的能量估计。
We are concerned with a two-phase flow system consisting of the Vlasov-Fokker-Planck equation for particles coupled to the compressible Euler equations for the fluid through the friction force. Global well-posedness of the Cauchy problem is established in perturbation framework, and rates of convergence of solutions toward equilibrium, which are algebraic in the whole space and exponential on torus, are also obtained under some additional conditions on initial data. The proof is based on the classical energy estimates.