论文标题
具有不确定性的多相Navier-Stokes-vlasov-Fokker-Planck系统的能量估计和低核分析
Energy estimates and hypocoercivity analysis for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainty
论文作者
论文摘要
本文与良好粒子状态中具有随机初始输入的KineITC流体模型有关，该模型是一个耦合不可压缩的Navier-Stokes方程和Vlasov-Fokker-Planck方程的系统，该系统模型分散了不同尺寸的颗粒。通过使用能量估计，在某些合适的SOBOLEV空间中建立了在全局平衡附近的随机初始数据的统一规则性，我们还通过低核心参数证明能量及时地衰减，这意味着该解决方案的长时间行为对初始数据中的随机扰动不敏感。对于该模型的广义多项式混乱随机盖尔金方法（GPC-SG），具有在全局平衡附近的初始数据，并且在物理和随机空间中足够平滑，我们证明GPC-SG方法具有光谱精度，时间均匀，时间均匀，并且误差数量呈指数式衰减。
This paper is concerned with a kineitc-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier-Stokes equations and the Vlasov-Fokker-Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation in the initial data. For the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the model, with initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Knudsen number, and the error decays exponentially in time.
