Upper bounds for the function solution of the homogenuous 2D Boltzmann equation with hard potential
Résumé
We deal with f t (dv), the solution of the homogeneous 2D Boltzmann equation without cutoff. The initial condition f 0 (dv) may be any probability distribution (except a Dirac mass). However, for sufficiently hard potentials , the semigroup has a regularization property (see Probab. Theory Related Fields 151 (2011) 659-704): f t (dv) = f t (v) dv for every t > 0. The aim of this paper is to give upper bounds for f t (v), the most significant one being of type f t (v) ≤ Ct −η e −|v| λ for some η, λ > 0.