# Compressible Flow and Euler's Equations.

Compressible Flow and Euler's Equations

Demetrios Christodoulou & Shuang Miao

International Press of Boston

PO Box 43502, Somerville, MA 02143

www.intlpress.com

9781571462978, \$58.00, www.amazon.com

In mathematics and physics, there is a large number of topics named in honor of Leonhard Euler, many of which include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. It has been said that, in an effort to avoid naming everything after Euler, discoveries and theorems are named after the first person after Euler to have discovered it. Compressible flow (gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Gases, but not liquids, display such behavior. To distinguish between compressible and incompressible flow in gases, the Mach number (the ratio of the speed of the flow to the speed of sound) must be greater than about 0.3 before significant compressibility occurs. The study of compressible flow is relevant to high-speed aircraft, jet engines, gas pipelines, commercial applications such as abrasive blasting, and many other fields. The ninth volume in the outstanding 'Surveys of Modern Mathematics' series from the International Press of Boston, "Compressible Flow and Euler's Equations" is a 581 page 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. Academicians and mathematicians Demetrios Christodoulou and Shuang Miao 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. Very strongly recommended for academic library Advanced Mathematics reference collections, "Compressible Flow and Euler's Equations" will be of particular interest to scholars and scientists working in partial differential equations in general and in fluid mechanics in particular.

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