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 \cite{[BF]}): $f_{t}(dv)=f_{t}(v)dv$ 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 $f_{t}(v)\leq Ct^{-\eta}e^{-\left\vert v\right\vert ^{\lambda}}$ for some $\eta,\lambda>0.$
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01593131
Contributor : Vlad Bally <>
Submitted on : Wednesday, May 2, 2018 - 12:39:40 PM
Last modification on : Thursday, July 18, 2019 - 3:00:05 PM
Long-term archiving on : Tuesday, September 25, 2018 - 12:04:10 AM

Files

AAP24April2018.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01593131, version 2
  • ARXIV : 1710.00695

Citation

Vlad Bally. Upper bounds for the function solution of the homogenuous 2D Boltzmann equation with hard potential. 2018. ⟨hal-01593131v2⟩

Share

Metrics

Record views

385

Files downloads

131