Mathematics of Open Fluid Systems

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

Part I: Modelling.- Mathematical Models of Fluids in Continuum Mechanics.- Open vs. Closed Systems.- Part II: Analysis.- Generalized Solutions.- Constitutive Theory and Weak-Strong Uniqueness Revisited.-Existence Theory, Basic Approximation Scheme.- Vanishing Galerkin Limit and Domain Approximation.-Vanishing Artificial Diffusion Limit.- Vanishing Artificial Pressure Limit.- Existence Theory - Main Results.-Part III: Qualitative Properties.- Long Time Behavior.- Statistical Solutions, Ergodic Hypothesis, and Turbulence.- Systems with Prescribed Boundary Temperature.

Details

Erscheinungsjahr:	2022
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxvii 284 S.
ISBN-13:	9783030947927
ISBN-10:	3030947920
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Novotný, Antonin Feireisl, Eduard
Auflage:	1st edition 2022
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	Antonin Novotný (u. a.)
Erscheinungsdatum:	02.04.2022
Gewicht:	0,476 kg