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

الأصل · EN

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*|βb((θ)) for β∈ (0,2] with (θ)= |v-v*|⁻¹(v-v*)· σ and σ∈ Sᵈ⁻¹, and assuming the classical cut-off condition b((θ)) integrable in Sᵈ⁻¹, we prove that there exists a > 0 such that moments with weight (a t,1 |v|β) are finite for t>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.