Bull. Korean Math. Soc. 2018; 55(2): 591-598
Online first article January 8, 2018 Printed March 30, 2018
https://doi.org/10.4134/BKMS.b170175
Copyright © The Korean Mathematical Society.
Meixia Xiao, Xianwen Zhang
Huazhong University of Science and Technology, Huazhong University of Science and Technology
This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term $\int_{\mathbb{R}^{n}}\rho\varphi dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data \cite{Kunzinger0001,Wei0001}. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of $\frac{4q-4}{3q-2}$ for $1 Keywords: Klein-Gordon field, Vlasov equation, weak solution, global existence MSC numbers: Primary 35Q83, 35D30, 82D10
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