无截止的玻尔兹曼方程的熵耗估计

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2022-08-06 DOI:10.3934/krm.2023006

Jamil Chaker, L. Silvestre

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引用次数: 3

摘要

用加权的L^p$-范数从下证明了玻尔兹曼碰撞算子的熵耗散的界。这个估计适用于广泛的电位，包括软电位和非常软电位。作为应用，我们研究了空间齐次Boltzmann方程的弱解，并证明了一个加权的$L^1_t(L^p_v)$估计。

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Entropy dissipation estimates for the Boltzmann equation without cut-off

We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted $L^p$-Norm. The estimate holds for a wide range of potentials including soft potentials as well as very soft potentials. As an application, we study weak solutions to the spatially homogeneous Boltzmann equation and prove a weighted $L^1_t(L^p_v)$ estimate.

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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.