The Navier-Stokes Equations

An Elementary Functional Analytic Approach
Softcover Nachdruck of the original 1. Auflage 2001
ISBN: 978-3-0348-9493-7
Verlag: Birkhäuser Basel

Buch, Englisch, 367 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 575 g

Reihe: Birkhäuser Advanced Texts Basler Lehrbücher

This book offers an elementary, self-contained approach to the mathematical theory of viscous, incompressible fluid in a domain of the Euclidian space, described by the equations of Navier-Stokes. It is the first to provide a systematic treatment of the subject. It is designed for students familiar with basic tools in Hilbert and Banach spaces, but fundamental properties of, for example, Sobolev spaces, are collected in the first two chapters.

Zielgruppe

Research

Autoren/Hrsg.

Sohr, Hermann

Fachgebiete

• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

I Introduction.- 1 Basic notations.- 2 Description of the functional analytic approach.- 3 Function spaces.- II Preliminary Results.- 1 Embedding properties and related facts.- 2 The operators ? and div.- 3 Elementary functional analytic properties.- III The Stationary Navier-Stokes Equations.- 1 Weak solutions of the Stokes equations.- 2 The Stokes operator A.- 3 The stationary Navier-Stokes equations.- IV The Linearized Nonstationary Theory.- 1 Preliminaries for the time dependent linear theory.- 2 Theory of weak solutions in the linearized case.- V The Full Nonlinear Navier-Stokes Equations.- 1 Weak solutions.- 2 Approximation of the Navier-Stokes equations.- 3 Existence of weak solutions of the Navier-Stokes system.- 4 Strong solutions of the Navier-Stokes system.