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Sharp decay estimates for the Vlasov-Poisson and Vlasov-Yukawa systems with small data

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  • In this paper, we present sharp decay estimates for small data solutions to the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a modification of the vector field method for transport equation as developed by Smulevici in 2016 for the Vlasov-Poisson system. Using the Green's function in particular to estimate the bilinear terms, we improve Smulevici's result by removing the requirement of some $ v $-weighted $ L^p $ integrability for the initial data and extend the result to the Vlasov-Yukawa system.

    Mathematics Subject Classification: Primary: 35Q83; Secondary: 35M31, 35B40.

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