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ISSN Imprimir: 2152-5080
ISSN On-line: 2152-5099
International Journal for Uncertainty Quantification
RANDOM REGULARITY OF A NONLINEAR LANDAU DAMPING SOLUTION FOR THE VLASOV-POISSON EQUATIONS WITH RANDOM INPUTS
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA
School of Mathematical Sciences, Institute of Natural Sciences, MOE-LSEC and SHL-MAC,
Shanghai Jiao Tong University, Shanghai 200240, China
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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