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Moment Propagation of the Vlasov-Poisson System with a Radiation Term

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Abstract

We investigate the dynamics of the Vlasov-Poisson system in the presence of radiation damping. A propagation result for velocity moments of order \(k>3\) is established in (Kunze and Rendall in Ann. Henri Poincaré 2:857–886, 2001). In this paper, we prove existence of global solutions propagating velocity and velocity-spatial moments of order \(k>2\) and establish an explicit polynomially growing in time bound on the moments.

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Notes

  1. Due to \(\Delta \geq \Delta _{0}(t)\), we have \(\frac{18C_{\ast }}{2^{n}-7}=I(t, \Delta _{0}(t)) \leq I(t, \Delta )=\frac{P}{2^{n}}\), i.e., \(P\geq \frac{18C_{\ast } \cdot 2^{n}}{2^{n}-7}\).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People’s Republic of China

    Meixia Xiao & Xianwen Zhang

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  1. Meixia Xiao
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  2. Xianwen Zhang
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Correspondence to Xianwen Zhang.

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Xiao, M., Zhang, X. Moment Propagation of the Vlasov-Poisson System with a Radiation Term. Acta Appl Math 160, 185–206 (2019). https://doi.org/10.1007/s10440-018-0200-3

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