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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019026936
pages 123-142

RANDOM REGULARITY OF A NONLINEAR LANDAU DAMPING SOLUTION FOR THE VLASOV-POISSON EQUATIONS WITH RANDOM INPUTS

Zhiyan Ding
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA
Shi Jin
School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China

RÉSUMÉ

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 by Hwang and Velázquez 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.

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