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Article Dans Une Revue The Annals of Applied Probability Année : 2019

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.

Dates et versions

hal-02429468 , version 2 (29-09-2017)
hal-02429468 , version 3 (02-05-2018)
hal-02429468 , version 1 (06-01-2020)

Identifiants

Citer

Vlad Bally. Upper bounds for the function solution of the homogenuous 2D Boltzmann equation with hard potential. The Annals of Applied Probability, 2019, 29, pp.1929 - 1961. ⟨10.1214/18-AAP1451⟩. ⟨hal-02429468v1⟩
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