Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty

TL;DR

This paper analyzes the sensitivity and convergence of Vlasov-Poisson-Boltzmann equations with uncertainties, establishing uniform energy estimates and justifying the incompressible Navier-Stokes-Poisson limit without Hilbert expansion.

Contribution

It extends uncertainty quantification to kinetic-fluid models with random initial data and provides the first precise convergence rate without Hilbert expansion.

Findings

Established uniform energy estimates with respect to the Knudsen number.

Proved the incompressible Navier-Stokes-Poisson limit with random inputs.

Achieved convergence rate without relying on Hilbert expansion.

Abstract

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.