与泊松方程耦合的可压缩粘性流体模型的广义解法

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-07-18 DOI:10.1063/5.0190282
Zhong Tan, Hui Yang
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引用次数: 0

摘要

本文论述了在具有 C2+α (0 < α < 1) 边界 ∂Ω 的有界域 Ω⊂R3 中与泊松方程耦合的可压缩粘性和气压流体模型。我们证明了绝热指数 γ > 1 时耗散解的存在性和弱强唯一性。我们发现当 γ∈(1,32) 时,泊松项 ρ∇Φ 不可积分。我们将充分利用泊松方程和能量不等式来克服这一困难。最后,我们得出ρ∇Φ会导致雷诺应力 R 的减小和能量耗散缺陷 E 的增大。
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Generalized solutions to the model of compressible viscous fluids coupled with the Poisson equation
This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Ω⊂R3 with C2+α (0 < α < 1) boundary ∂Ω. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent γ > 1. We find that the Poisson term ρ∇Φ is not integrable when γ∈(1,32). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that ρ∇Φ leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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