A new approach to the creation and propagation of exponential moments in the Boltzmann equation

We study the creation and propagation of exponential moments of solutions to the spatially homogeneous d-dimensional Boltzmann equation. In particular, when the collision kernel is of the form |v-v*|^beta b(s() for beta in (0,2] with s(= |v-v*|^-1(v-v*)ot sigma and sigma in S^d-1, and assuming the classical cut-off condition b(s() integrable in S^d-1, we prove that there exists a gt; 0 such that moments with weight a t,1 |v|^ are finite for tgt;0, where a only depends on the collision kernel and the initial mass and energy. We propose a novel method of proof based on a single differential inequality for the exponential moment with time-dependent coefficients.