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June 2019 Upper bounds for the function solution of the homogeneous 2D Boltzmann equation with hard potential
Vlad Bally
Ann. Appl. Probab. 29(3): 1929-1961 (June 2019). DOI: 10.1214/18-AAP1451

Abstract

We deal with ft(dv), the solution of the homogeneous 2D Boltzmann equation without cutoff. The initial condition f0(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): ft(dv)=ft(v)dv for every t>0. The aim of this paper is to give upper bounds for ft(v), the most significant one being of type ft(v)Ctηe|v|λ for some η,λ>0.

Citation

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Vlad Bally. "Upper bounds for the function solution of the homogeneous 2D Boltzmann equation with hard potential." Ann. Appl. Probab. 29 (3) 1929 - 1961, June 2019. https://doi.org/10.1214/18-AAP1451

Information

Received: 1 May 2018; Revised: 1 August 2018; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057471
MathSciNet: MR3914561
Digital Object Identifier: 10.1214/18-AAP1451

Subjects:
Primary: 60H07 , 60J75 , 82C40

Keywords: Boltzmann equation without cutoff , Hard potentials , integration by parts , interpolation criterion

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 3 • June 2019
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