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 $1<q<2$. As a consequence, global existence of weak solutions for general initial data is obtained.
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 $1<q<2$. As a consequence, global existence of weak solutions for general initial data is obtained.
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