Synopses & Reviews
This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. the book is concerned with geometric problems for Hele-Shaw flows. Additionally, Hele-Shaw flows on parameter spaces are discussed, and connections with string theory are revealed. Assumes a graduate level understanding of real and complex analysis, and fluid mechanics.
Synopsis
This monograph aims at giving a presentation of recent and new ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. In particular, this book is concerned with geometric problems for Hele-Shaw flows. Also Hele-Shaw flows on parameter spaces (e.g., the Teichmuller space) are treated and connections with string theory are revealed. Ultimately, the interaction between several branches of complex and potential analysis, and planar fluid mechanics is discussed.
For most parts of this book the background provided by graduate courses in real and complex analysis, in particular, the theory of conformal mappings and in fluid mechanics is assumed. There are some historical remarks concerning the people that have contributed to the topic. The book is as self-contained as possible.
Table of Contents
Introduction.- Explicit Strong Solutions.- Weak Solutions and Balayage.- Geometric Properties.- Capacities and Isoperimetric Inequalities.- General Evolution Equations.- Hele-Shaw Evolution and Strings.