Compressible flow and Euler's equations
Compressible flow and Euler's equations
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发表时间：
2012-12
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通讯作者：
D. Christodoulou;Shuang Miao
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作者：
D. Christodoulou;Shuang Miao
这本专著考虑了三维空间中具有任意状态方程的经典可压缩欧拉方程，其初始数据对应于球外的恒定状态。在适当限制初始偏离常态的大小的情况下，建立了完整描述最大发展的定理。特别地，最大解域的边界包含一个奇异部分，波前密度在这里爆炸并形成激波。作者得到了这一奇异边界的详细几何描述，并详细分析了那里的解的行为。这种方法是几何的，中心概念是声学时空流形。与第一作者处理相对论流体的专著相比，这本专著不仅给出了更简单和完备的证明，而且还加强了一些结果。此外，它还深入解释了该方法所基于的想法。此外，还讨论了仅与非相对论理论有关的某些几何问题。一般研究偏微分方程组的学者，特别是流体力学的学者，会对可压缩流动和欧拉方程感兴趣。
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 EulerAEs Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular.