Navier-Stokes Equations
Navier-Stokes Equations
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DOI：
10.1090/chel/343
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发表时间：
1977-02
期刊：
影响因子：
--
通讯作者：
R. Temam
中科院分区：
文献类型：
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作者：
R. Temam
最初出版于1977年，这本书致力于粘性不可压缩流体的Navier-Stokes方程的理论和数值分析。在理论方面，结果有关的存在性，唯一性，并在某些情况下，正则性的解决方案。在数值方面，各种方法的近似Navier-Stokes问题的离散化被认为是，如有限的引用方法，有限元方法，和分数步方法。数值方法的稳定性和收敛性问题被尽可能完整地处理。本书中的新材料（与1984年前一版相比）是一个附录，转载了1998年撰写的一篇调查文章。本附录涉及到一些在早期版本中没有涉及的方面，特别是从连续介质力学的基本守恒原理推导出的纳维-斯托克斯方程，进一步的历史观点，以及该领域新发展的迹象。附录中还概述了有关的欧拉方程和可压缩Navier-Stokes方程的一些方面。这本书是以教科书的风格写的，作者试图使治疗自成一体。它可以作为研究人员的教科书或参考书。准备阅读这本书包括一些熟悉的Navier-Stokes方程和一些知识的功能分析和Sololev空间。
Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.