Open AccessLower bound for the Boltzmann equation whose regularity grows tempered with time
Author(s) -
Lingbing He,
Jie Ji,
Ling-Xuan Shao
Publication year - 2021
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2021020
Subject(s) - boltzmann equation , bounded function , boltzmann's entropy formula , sobolev space , lattice boltzmann methods , entropy (arrow of time) , work (physics) , mathematics , boltzmann constant , stability (learning theory) , energy (signal processing) , physics , statistical physics , upper and lower bounds , mathematical analysis , thermodynamics , computer science , statistics , machine learning
As a first step towards the general global-in-time stability for the Boltzmann equation with soft potentials, in the present work, we prove the quantitative lower bounds for the equation under the following two assumptions, which stem from the available energy estimates, i.e. (ⅰ). the hydrodynamic quantities (local mass, local energy, and local entropy density) are bounded (from below or from above) uniformly in time, (ⅱ). the Sobolev regularity for the solution grows tempered with time.