Solutions of the spatially homogeneous Boltzmann equation with time-dependent Lorentz force term

We obtain a certain transformation relating the solutions of the space-uniform Boltzmann equation with the Lorentz force term to those of the Boltzmann equation without external force. This enables us, in the case of angular cut-off intermolecular potentials, to prove the global existence, uniqueness and positivity of strict solutions for the former equation by means of known results on the latter one.