库仑碰撞动力学模型的希尔伯特扩展

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED Quarterly of Applied Mathematics Pub Date : 2024-03-12 DOI:10.1090/qam/1689

Zhimeng Ouyang, Lei Wu, Qinghua Xiao

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引用次数: 0

摘要

相对论弗拉索夫-麦克斯韦-朗道（r-VML）系统和相对论朗道（r-LAN）方程是描述电子气体动力学的基本模型。本文介绍了一种新颖的加权能量法，并建立了单种 r-VML 系统和 r-LAN 方程的希尔伯特展开的有效性。当努森数缩小为零时，我们分别严格证明了相对论欧拉-麦克斯韦极限和相对论欧拉极限。这成功地解决了关于朗道方程流体力学极限的长期未决问题。

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Hilbert expansion for Coulomb collisional kinetic models

The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau (r-LAN) equation are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the one-species r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.