具有正则耗散函数的静态 Navier-Stokes-Boussinesq 系统

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-15 DOI:10.1134/s0001434624050031

E. S. Baranovskii

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引用次数: 0

摘要

摘要我们研究了一个数学模型的边界值问题，该数学模型描述了粘性流体在具有局部 Lipschitz 边界的三维（或二维）有界域中的非等温稳态流动。这里考虑的传热和传质模型的特点是在能量平衡方程中使用了正则化的瑞利耗散函数。这样就可以将粘性摩擦效应引起的能量耗散考虑在内。在模型数据的自然假设下，证明了弱解存在的定理。此外，我们还建立了额外的条件，保证弱解是唯一的和/或强的。

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The Stationary Navier–Stokes–Boussinesq System with a Regularized Dissipation Function

Abstract

We study a boundary value problem for a mathematical model describing the nonisothermal steady-state flow of a viscous fluid in a 3D (or 2D) bounded domain with locally Lipschitz boundary. The heat and mass transfer model considered here has the feature that a regularized Rayleigh dissipation function is used in the energy balance equation. This permits taking into account the energy dissipation due to the viscous friction effect. A theorem on the existence of a weak solution is proved under natural assumptions on the model data. Moreover, we establish extra conditions guaranteeing that the weak solution is unique and/or strong.

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来源期刊

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.