Upper bounds for the function solution of the homogenuous 2D Bolzmann equation with hard potential
Résumé
We deal with f t (dv); solution of the homogenuous 2D Bolzmann equation without cuto¤. An important point is that the initial condition f 0 (dv) may be any probability distribution (except a Dirac mass). However, for su¢ cientely hard potentials, the semigroup has a regularization property (see [5]): 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 more signi…cant one beeing f t (v) Ct e jvj for some ; > 0:
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