Local solutions to the initial and initial boundary value problem for the Boltzmann equation with an external force. I (Q1061579)

In this paper we show the local existence of solutions to the initial and initial boundary value problem of the Boltzmann equation with an external force and a general (hard or soft) angular cutoff scattering potential. The initial data may be arbitrary large in some function spaces and the solution exists in a time interval corresponding to the size of the initial data. Our method is a combination of those of \textit{A. Glikson} [e.g.: Arch. Ration. Mech. Anal. 47, 389-394 (1972; Zbl 0247.76067)] and \textit{S. Kaniel} and \textit{M. Shinbrot} [Commun. Math. Phys. 58, 65-84 (1978; Zbl 0371.76061)] to some extent, but simpler and more natural.