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arXiv · 1805.10837

Decay estimates for the $3D$ relativistic and non-relativistic Vlasov-Poisson systems

Xuecheng Wang
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Abstract

We study the small data global regularity problem of the $3D$ Vlasov-Poisson system for both the relativistic case and the non-relativistic case. The main goal of this paper is twofold. (i) Based on a Fourier method, which works systematically for both the relativistic case and the non-relativistic case, we give a short proof for the global regularity and the sharp decay estimate for the $3D$ Vlasov-Poisson system. Moreover, we show that the nonlinear solution scatters to a linear solution in both cases. The result of sharp decay estimates for the non-relativistic case is not new, see Hwang-Rendall-Vel\'azquez and Smulevici. (ii) The Fourier method presented in this paper serves as a good comparison for the study of more complicated $3D$ relativistic Vlasov-Nordstr\"om system and $3D$ relativistic Vlasov-Maxwell system.

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Xuecheng Wang. 2018-05-28. Decay estimates for the $3D$ relativistic and non-relativistic Vlasov-Poisson systems. https://arxiv.org/abs/1805.10837

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