Lower bound for the Boltzmann equation whose regularity grows tempered with time

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2021-01-01 DOI:10.3934/krm.2021020

Lingbing He, Jie Ji, Ling-Xuan Shao

引用次数: 0

Abstract

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.

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玻尔兹曼方程的下界，其规律性随时间而变弱

作为研究具有软势的玻尔兹曼方程的一般全局时间稳定性的第一步，在本文中，我们在以下两个假设下证明了该方程的定量下界，这两个假设源于可用的能量估计，即(ⅰ)。水动力量(局部质量、局部能量和局部熵密度)在时间上均匀地(从下或从上)有界，(ⅱ)。解的Sobolev规律性随着时间的推移而变弱。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.