Random Regularity of the Vlasov-Poisson System with Random Initial Inputs in the Quasineutral Regime

Abstract

The Vlasov-Poisson system is widely used in plasma physics and other related fields. In this paper, we study the Vlasov-Poisson system with initial uncertainty in the quasineutral regime. First, we prove the uniform convergence in the Wasserstein distance between the uncertain Vlasov-Poisson system in the quasineutral regime and its quasineutral limit system with random initial inputs. This is achieved by deriving an upper bound for the Wasserstein distance and rigorously estimating each component of this bound. Furthermore, by defining a new norm with respect to the quasineutral parameter and estimating the distribution function as well as the electric field in this norm using a variable substitution, we establish the random regularity of the solutions in the quasineutral regime. This work develops a novel framework for quantifying the propagation of the initial uncertainty of the Vlasov-Poisson system in the quasineutral regime, providing a theoretical basis for designing high-performance numerical algorithms.