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Birkhäuser

Mathematics of Open Fluid Systems

  • Book
  • © 2022

Overview

Authors:
  1. Eduard Feireisl

    1. Institute of Mathematics, Czech Academy of Sciences, Praha, Czech Republic

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  2. Antonin Novotný

    1. Carqueiranne, France

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  • 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 the statistical theory of turbulence and the validity of the ergodic hypothesis

Part of the book series: Nečas Center Series (NECES)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xxvii
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  2. Modelling

    1. Front Matter

      Pages 1-1
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    2. Mathematical Models of Fluids in Continuum Mechanics

      • Eduard Feireisl, Antonin Novotný
      Pages 3-11

    3. Open vs. Closed Systems

      • Eduard Feireisl, Antonin Novotný
      Pages 13-21

  3. Analysis

    1. Front Matter

      Pages 23-24
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    2. Generalized Solutions

      • Eduard Feireisl, Antonin Novotný
      Pages 25-61

    3. Constitutive Theory and Weak–Strong Uniqueness Revisited

      • Eduard Feireisl, Antonin Novotný
      Pages 63-82

    4. Existence Theory, Basic Approximation Scheme

      • Eduard Feireisl, Antonin Novotný
      Pages 83-106

    5. Vanishing Galerkin Limit and Domain Approximation

      • Eduard Feireisl, Antonin Novotný
      Pages 107-140

    6. Vanishing Artificial Diffusion Limit

      • Eduard Feireisl, Antonin Novotný
      Pages 141-159

    7. Vanishing Artificial Pressure Limit

      • Eduard Feireisl, Antonin Novotný
      Pages 161-194

    8. Existence Theory: Main Results

      • Eduard Feireisl, Antonin Novotný
      Pages 195-201

  4. Qualitative Properties

    1. Front Matter

      Pages 203-203
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    2. Long Time Behaviour

      • Eduard Feireisl, Antonin Novotný
      Pages 205-231

    3. Statistical Solutions, Ergodic Hypothesis, and Turbulence

      • Eduard Feireisl, Antonin Novotný
      Pages 233-239

    4. Systems with Prescribed Boundary Temperature

      • Eduard Feireisl, Antonin Novotný
      Pages 241-260

  5. Back Matter

    Pages 261-284
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Keywords

About this book

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.

Reviews

“This book deals with issues related to the delicate problem of open fluid systems, where by open system we mean a system in which an exchange of matter and/or energy can take place with the surrounding environment. The topic is extremely current and relevant … . it is unique in its kind and can represent the starting point for studies and reflections in the field of open systems.” (Francesca Brini, Mathematical Reviews, August, 2023)



“This book may be useful to scientists working in the field of hydrodynamics, and the authors were successful in putting their brick into the building of fluid mechanics.” (Aleksey Syromyasov, zbMATH 1504.76003, 2023)

Authors and Affiliations

  • Institute of Mathematics, Czech Academy of Sciences, Praha, Czech Republic

    Eduard Feireisl

  • Carqueiranne, France

    Antonin Novotný

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