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Upper bounds for the function solution of the homogenuous 2D Boltzmann equation with hard potential

Vlad Bally 1, 2
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : 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.
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Submitted on : Monday, January 6, 2020 - 4:22:55 PM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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

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