A mathematical introduction to fluid mechanics
type: Item
instance of: scholarly article
title: A mathematical introduction to fluid mechanics
zbMATH Open document ID: 0417.76002
DOI: 10.1007/978-1-4684-0082-3
author: J. E. Marsden
author: Alexandre J. Chorin
published in: Universitext
publication date: 1979-01-01T00:00:00Z
review text: The present book originated in a course in fluid mechanics taught in the Department of Mathematics of the University of California, Berkeley in Spring 1978. Like all the other books and papers written by J. E. Marsden as author or co-author it is highly recommendable to read, especially to those who are Interested in a rigorous mathematical treatment of fluid mechanics. The book written by A. J. Chorin and J. E. Marsden provides an easy readable introduction to fluid mechanics although it covers most of the subject contained in ordinary physics books. Chapter one deals with isentropic flows and the Euler equations. The usual conservation laws and vorticity theorems are treated and the Navier-Stokes equations for incompressible flows are introduced. The second chapter is concerned with potential and slightly viscous flows. Worth mentioning -- because unusual for introductory books -- is the part, where the connection between vorticitiy flows, Hamiltonian systems and Lie groups is pointed out. Then the Prandtl boundary layer equations are discussed. Finally the theory of vortex sheets is presented utilizing some concepts from probability theory. In the last chapter the authors give a short survey of the fundamentals of compressible flows. This is according to the reviewer's opinion the most interesting part of the book. It contains a very clarifying introduction to shock waves and weak solutions of partial differential equations, which in standard physics books is in general not treated in full mathematical rigor. What makes the books so valuable to newcomers in the field of fluid mechanics is the successful combination of Physics and Mathematics. Showing this link maintains the authors' main intention throughout the book.
Mathematics Subject Classification ID: 76-01
Mathematics Subject Classification ID: 76Bxx
Mathematics Subject Classification ID: 76Dxx
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35Q31
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 3650164
zbMATH Keywords: fluid mechanics
zbMATH Keywords: isentropic flows
zbMATH Keywords: Euler equations
zbMATH Keywords: conservation laws
zbMATH Keywords: vorticity theorems
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: potential flows
zbMATH Keywords: slightly viscous flows
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Lie groups
zbMATH Keywords: shock waves
zbMATH Keywords: weak solutions
zbMATH Keywords: Riemann problem
zbMATH Keywords: gas flow in one dimension
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-1-4684-0082-3
OpenAlex ID: W2005780385
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description: scientific article; zbMATH DE number 3650164