论文标题
敏感性分析和不确定性的Vlasov-Poisson-Boltzmann方程的不可压缩的Navier-Stokes-Poisson极限
Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty
论文作者
论文摘要
对于从初始数据或碰撞内核中随机不确定性的vlasov-Poisson-Boltzmann方程，我们使用低调方法证明了敏感性分析和能量均匀地相对于knudsen数量的能量估计。结果，我们还通过随机输入证明了不可压缩的Navier-Stokes-poisson限制。特别是，我们首次获得了基于希尔伯特（Hilbert）扩展的任何结果，而无需使用任何结果，就获得了精确的收敛率{\ em}。我们不仅将先前的确定性Navier-Stokes-Poisson限制概括为随机初始数据案例，还将先前的不确定性定量结果改善了初始数据包括动力学和流体零件。
For the Vlasov-Poisson-Boltzmann equations with random uncertainties from the initial data or collision kernels, we proved the sensitivity analysis and energy estimates uniformly with respect to the Knudsen number in the diffusive scaling using hypocoercivity method. As a consequence, we also justified the incompressible Navier-Stokes-Poisson limit with random inputs. In particular, for the first time, we obtain the precise convergence rate {\em without} employing any results based on Hilbert expansion. We not only generalized the previous deterministic Navier-Stokes-Poisson limits to random initial data case, also improve the previous uncertainty quantification results to the case where the initial data include both kinetic and fluid parts.
