International Journal for Uncertainty Quantification

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

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 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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