The goal of this text is to present some of the basic ideas of fluid mechanics in a mathematically attractive manner, to present the physical background and motivation for some constructions that have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems and to interest some of the students in this beautiful and difficult subject. The third edition has incorporated a number of updates and revisions, but the spirit and scope of the original book are unaltered.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematIcs. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts tn Applted Mathematzcs (TAM).

The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.

TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Apphed Mathematzcal Saences (AMS) series, which will focus on advanced textbooks and research level monographs.