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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 $f_{t}(dv)$, 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 $f_{t}(v)\leq Ct^{-\eta}e^{-\vert v\vert^{\lambda}}$ for some $\eta,\lambda>0$.

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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

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2019
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