On solutions and higher moments for the linear Boltzmann equation with infinite range forces

This paper considers an integral form of the linear, space-inhomogeneous Boltzmann equation with infinite-range forces in the collision term, and with periodic boundary conditions. The existence of a measure solution is proved in the case of hard-potential forces including kth power forces with k 3 = 5. The solution conserves mass and has bounded energy. Also, higher moments of the solution remain globally bounded in time, if they exist initially. In the course of the proof, some collision estimates for the velocities are obtained. THE LINEAR Boltzmann transport equation is frequently used for mathematical modelling in physics, geophysics, and astrophysics. This paper studies the linear transport equation for a distribution function f(x, v, t) (describing for instance a neutron distribution) depending on a space-variable x = {xx, x2, x3) in a nonmul