Force stability of the Boltzmann equations

Source abstract

In this paper, we consider the Boltzmann equation with external force in the whole space, where the collision kernel is assumed to be hard potential and cutoff. We prove that the solutions of such Boltzmann equations are [Formula: see text] ([Formula: see text]) stable under the perturbation of external force. Our estimate is based on the gradient estimate of the solution. The key step of this paper is to estimate the solutions of the equations propagate in different forward bi-characteristic.