A Mathematical Introduction to Fluid Mechanics

  • A. J. Chorin
  • J. E. Marsden

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-vii
  2. A. J. Chorin, J. E. Marsden
    Pages 1-62
  3. A. J. Chorin, J. E. Marsden
    Pages 63-127
  4. A. J. Chorin, J. E. Marsden
    Pages 128-205

About this book

Introduction

These notes are based on a one-quarter (i. e. very short) course in fluid mechanics taught in the Department of Mathematics of the University of California, Berkeley during the Spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima­ tion procedures. The goals were: (i) to present some of the basic ideas of fluid mechanics in a mathematically attractive manner (which does not mean "fully rigorous"); (ii) to present the physical back­ ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; (iil. ) 'to interest some of the students in this beautiful and difficult subject. The notes are divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented; it is hoped that it helps to clarify the ideas. The third chapter contains an analysis of one-dimensional gas iv flow, from a mildly modern point of view. Weak solutions, Riemann problems, Glimm's scheme, and combustion waves are discussed. The style is informal and no attempt was made to hide the authors' biases and interests.

Keywords

Navier-Stokes equation Potential fluid mechanics mechanics waves

Authors and affiliations

  • A. J. Chorin
    • 1
  • J. E. Marsden
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0082-3
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90406-1
  • Online ISBN 978-1-4684-0082-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book