Compressible Flow and Euler s Equations (Surveys of Modern Mathematics) - Softcover

Christodoulou, Demetrios; Miao, Shuang

Softcover

ISBN 10: 157146297X ISBN 13: 9781571462978

Publisher: International Press, 2014

Synopsis

This monograph considers the classical compressible Euler Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, the authors establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the density of the wave fronts blows up and shocks form. The authors obtain a detailed description of the geometry of this singular boundary, and a detailed analysis of the behavior of the solution there. The approach is geometric, the central concept being that of the acoustical spacetime manifold.

Compared to a previous monograph treating the relativistic fluids by the first author, the present monograph not only gives simpler and self-contained proofs but also sharpens some of the results. In addition, it explains in depth the ideas on which the approach is based. Moreover, certain geometric aspects which pertain only to the non-relativistic theory are discussed.

Compressible Flow and Euler’s Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular.

About this title

About the Author

Demetrios Christodoulou, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland.

Shuang Miao, Department of Mathematics, University of Michigan, USA.

Edition details

• Publisher: International Press
• Publication date: 2014
• Language: English
• ISBN 10: 157146297X
• ISBN 13: 9781571462978
• Binding: Paperback
• Number of pages: 602