Mathematical Aspects of Subsonic and Transonic Gas Dynamics

This concise volume by a prominent mathematician offers an important survey of mathematical aspects of the theory of compressible fluids. The treatment is geared toward advanced undergraduates and graduate students in physics, applied mathematics, and engineering. Focusing on two-dimensional steady potential flows, the text eschews detailed proofs in favor of clear indications of the main ideas and descriptions of new mathematical concepts and methods that arose in connection with these chapters in fluid dynamics.
Starting with a general discussion of the differential equations of a compressible gas flow, the book advances to the mathematical background of subsonic flow theory. Subsequent chapters explore the behavior of a flow at infinity and methods for the determination of flows around profiles, flows in channels and with a free boundary, the mathematical background of transonic gas dynamics, and some problems in transonic flow. An extensive bibliography of 400 papers concludes the text.

Latvian mathematician Lipman Bers (1914–93) emigrated to the United States in 1940 and taught at Brown, Syracuse, and NYU before joining the Columbia faculty from 1964–82. He created the theory of pseudoanalytic functions and worked in many other areas, including Riemann surfaces and Kleinian groups. Bers was also a prominent human rights activist who helped obtain the release of Soviet dissidents during the 1970s.

Introduction1. The differential Equations of a potential gas Flow2. Mathematical Background of Subsonic Flow Theory3. Some Problems in Subsonic4. Mathematical Background of trasonic Gas Dynamics5. Some Problems in Transonic FlowAppendixBibliographyIndex