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Titlebook: Mathematics of Open Fluid Systems; Eduard Feireisl,Antonin Novotný Book 2022 The Editor(s) (if applicable) and The Author(s), under exclus

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发表于 2025-3-21 18:58:41 | 显示全部楼层 |阅读模式
书目名称Mathematics of Open Fluid Systems
编辑Eduard Feireisl,Antonin Novotný
视频video
概述Presents a mathematical theory of open fluid systems in the context of continuum thermodynamics.Develops a concept of weak solutions based on entropy rather than the energy balance equation.Considers
丛书名称Nečas Center Series
图书封面Titlebook: Mathematics of Open Fluid Systems;  Eduard Feireisl,Antonin Novotný Book 2022 The Editor(s) (if applicable) and The Author(s), under exclus
描述The goal of this monograph is to develop a mathematical theory of open fluid systems in the framework of continuum thermodynamics. Part I discusses the difference between open and closed fluid systems and introduces the Navier-Stokes-Fourier system as the mathematical model of a fluid in motion that will be used throughout the text. A class of generalized solutions to the Navier-Stokes-Fourier system is considered in Part II in order to show existence of global-in-time solutions for any finite energy initial data, as well as to establish the weak-strong uniqueness principle.  Finally, Part III addresses questions of asymptotic compactness and global boundedness of trajectories and briefly considers the statistical theory of turbulence and the validity of the ergodic hypothesis.
出版日期Book 2022
关键词Mathematical Fluid Mechanics; Open Fluid Systems; Navier-Stokes-Fourier System; Ergodic Hypothesis; Stat
版次1
doihttps://doi.org/10.1007/978-3-030-94793-4
isbn_softcover978-3-030-94792-7
isbn_ebook978-3-030-94793-4Series ISSN 2523-3343 Series E-ISSN 2523-3351
issn_series 2523-3343
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 20:25:35 | 显示全部楼层
Existence Theory, Basic Approximation Scheme equilibrium. As many problems related to turbulence are formulated in terms of global in time or even entire (defined for any time . ∈ .) solutions, the existence theory in the framework of weak solutions represents a suitable platform to attack them in a rigorous manner.
发表于 2025-3-22 02:53:08 | 显示全部楼层
Existence Theory: Main Results preceding four chapters and formulate the main results concerning the existence of weak solutions. Although we have systematically considered a compact time interval [0, .], . > 0, the extension to [0, .) is straightforward.
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Constitutive Theory and Weak–Strong Uniqueness Revisitedypotheses imposed on the equation of state as well as the transport coefficients and establish a general weak–strong uniqueness principle valid in the class of finite energy weak solutions. The same set of hypotheses will guarantee the existence of global in time weak solutions for any finite energy/entropy initial data.
发表于 2025-3-22 20:56:12 | 显示全部楼层
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Systems with Prescribed Boundary Temperatureux on the inflow part of the boundary, and Robin type boundary conditions for the heat flux. Other types of boundary conditions could be handled in the same manner as long as the total energy flux through the boundary is controlled. Apparently this is not the case if the temperature instead of the heat flux is prescribed on the boundary.
发表于 2025-3-23 02:42:56 | 显示全部楼层
Book 2022tence of global-in-time solutions for any finite energy initial data, as well as to establish the weak-strong uniqueness principle.  Finally, Part III addresses questions of asymptotic compactness and global boundedness of trajectories and briefly considers the statistical theory of turbulence and the validity of the ergodic hypothesis.
发表于 2025-3-23 06:09:36 | 显示全部楼层
https://doi.org/10.1007/978-3-030-94793-4Mathematical Fluid Mechanics; Open Fluid Systems; Navier-Stokes-Fourier System; Ergodic Hypothesis; Stat
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