非等温麦克斯韦-斯特凡系统弱解的全局存在性和弱-强唯一性 *

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-05-27 DOI:10.1088/1361-6544/ad4c49
Stefanos Georgiadis and Ansgar Jüngel
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引用次数: 0

摘要

麦克斯韦-斯特凡方程用质量扩散和热传导描述了重心速度消失的多组分气体混合物的动力学。该方程由质量和能量平衡组成,并与一个代数系统相耦合,该代数系统将部分速度和驱动力联系起来。利用有界熵法证明了该系统在具有无流动边界条件的有界域中弱解的全局存在性。先验估计从熵不等式中获得,而熵不等式源于一致的热力学模型。此外,还利用相对熵方法证明了条件弱-强唯一性。
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Global existence of weak solutions and weak–strong uniqueness for nonisothermal Maxwell–Stefan systems *
The dynamics of multicomponent gas mixtures with vanishing barycentric velocity is described by Maxwell–Stefan equations with mass diffusion and heat conduction. The equations consist of the mass and energy balances, coupled to an algebraic system that relates the partial velocities and driving forces. The global existence of weak solutions to this system in a bounded domain with no-flux boundary conditions is proved by using the boundedness-by-entropy method. A priori estimates are obtained from the entropy inequality which originates from the consistent thermodynamic modelling. Furthermore, a conditional weak–strong uniqueness property is shown by using the relative entropy method.
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来源期刊
Nonlinearity
Nonlinearity 物理-物理:数学物理
CiteScore
3.00
自引率
5.90%
发文量
170
审稿时长
12 months
期刊介绍: Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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