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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019026936
Forthcoming Article

Random regularity of a nonlinear Landau Damping solution for the Vlasov-Poisson equations with random inputs

Shi Jin
University of Wisconsin-Madison
Zhiyan Ding
University of Wisconsin-Madison

ABSTRACT

In this paper, we study the nonlinear Landau damping solution of the Vlasov-Poisson equations with random inputs from the initial data or equilibrium. For the solution studied in [H.J. Hwang and J. J.L.Velazquez, Indiana University Mathematics Journal, Vol. 58, No. 6, 2009], we prove that the solution depends smoothly on the random input, if the long-time limit distribution function has the same smoothness, under some smallness assumptions. We also establish the decay of the higher-order derivatives of the solution in the random variable, with the same decay rate as its deterministic counterpart.