带德拜-汤川势能的均质玻尔兹曼方程的量值解的存在性和平滑效应

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI:10.1137/23m1562123

Shuaikun Wang, Tong Yang

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 5 期，第 5969-5994 页，2024 年 10 月。摘要在本文中，我们考虑了具有德拜-尤卡瓦势的均相玻尔兹曼方程的量值解。首先，对于真正的德拜-尤卡瓦势，我们证明了具有矩增益等性质的解的全局时间存在性。然后，我们考虑 Deybe-Yukawa 型势能的 Maxwellian 分子。通过引入新的矫顽力估计，我们证明了只要初始数据[math]不与度量本身的两个平移正交，解[math]对于任何[math]都是存在的。

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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Existence and Smoothing Effect of Measure Valued Solution to the Homogeneous Boltzmann Equation with Debye–Yukawa Potential

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5969-5994, October 2024.
Abstract. In this paper, we consider the measure valued solution to the homogeneous Boltzmann equation with Debye–Yukawa potential. First, for the case of the true Debye–Yukawa potential, we prove global in time existence of a solution with properties such as gain of moments. And then we consider the Maxwellian molecule of Deybe–Yukawa type potential. By introducing a new coercivity estimate, we show that the solution [math] for any [math], as long as the initial data [math] is not orthogonal to two translations of the measure itself.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.