〖求助〗请问那本教材中有关于n-s方程组稳定性分析的内容

yuarmy

因为需要对提出的方法作一点理论分析的工作，因此需要了解一下这方面的知识，各位朋友，请提供一些关于n-s方程组稳定性，相容性和收敛性方面内容的书记和论文。谢谢各位朋友了。

turbulencest

I remember book by zhongshan university covered this topic

windsnow

Drazin, P. G., and W. H. Reid, 1981: Hydrodynamic Stability. Cambridge Univ. Press, Cambridge, 527 pp.
Parks, P, C., and V. Hahn, 1993: Stability theory. Prentice Hall, New York, 150 pp.

zouchu

我也想知道相关的内容,Drazin & Reid 的书里面只有最后部分提及了一点点非线性稳定性的问题,好像还有很新的书,但不知道名字了.
最好是哪位知道如何将分叉理论完整地应用到n-s方程的书?
从没有流动,到定常流动分叉,从定常流动到振荡分叉,从振荡流动到非周期混沌分叉,
讲得比较系统一点的书有没有啊?

windsnow

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Drazin & Reid 的书里面只有最后部分提及了一点点非线性稳定性的问题,好像还有很新的书
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The following book is highly recommended:
Swater, G. E., 2000: Introduction to Hamiltonian Fluid Dynamics and Stability Theory. Chapman & Hall/CRC, New York, 274 pp.
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A Few Important References on Hamiltonian Fluid Dynamics and Nonlinear Stability and Instability:
Abarbanel, H. D. I., D. D. Holm, J. E. Marsden and T. S. Ratiu, 1986: Nonlinear stability analysis of stratified fluid equilibria. Phil. Trans. R. Soc. Lond. A, 318, 349-409.
Arnol'd, V. I., 1965: Conditions for nonlinear stability of stationary plane curvilinear flows of an ideal fluid. Doklady  Mat. Nauk., 162, 773-777.
Arnol'd, V. I., 1965: Variational principle for three dimensional steady-state flows of an ideal fluid. Prikl. Mat. Mekh., 29, 846-851. Translated in J. Appl. Math. Mech., 29, 1002-1008.
Arnol'd, V. I., 1966: On an a priori estimate in the theory of hydrodynamical stability. Izv. Vyssh. Uchebn. Zaved. Matematika, 54, no. 5, 3-5. (English Transl: Am. Math. Soc. Transl., 79 (1969), 267-269.)
Arnol’d, V. I., 1978: Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.
Craik, A. D. D., 1985: Wave Interactions and Fluid Flows. Cambridge Univ. Press, Cambridge, 322 pp.
Holm, D. D., J. E. Marsden, T. Ratiu and A Weinstein, 1985: Nonlinear stability of fluid and plasma equilibria. Physics Reports, 123, 1-116.
Kadomtsev, B. B., 1965: Plasma Turbulence. Academic Press, New York, 149 pp.
McIntyre, M. E., and T. G. Shepherd, 1987: An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd 's stability theorems. J. Fluid Mech., 181, 527-565.
Salmon, R., 1988: Hamiltonian fluid mechanics. Ann. Rev. Fluid Mech., 20, 225-256.
Yuen, H. C., and B. M. Lake, 1982: Nonlinear dynamics of deep-water gravity waves. Advances in Appl. Mech., 22, 67-229.
Zakharov, V. E., 1967: The instability of waves in nonlinear dispersive media. Sov. Phys. JETP, 24, 740-744.
Zakharov, V. E., 1968: Stability of periodic waves of finite amplitude on the surface of a deep fluid. Zh. Prikl. Mekh. Fiz.. 9, 86. (Engl. transl. J. Appl. Mech. Tech. Phys., 9, 190-194.)
Zakharov, V. E., 1974: Hamiltonian formalism for waves in nonlinear media with dispersion. Izv. vuzov. Radiofizika, 17, 431-453.  

windsnow

哦，对了，下面一本中文书也有一部分介绍非线性流体稳定性理论。
黄思训，伍荣生编著，2001：大气科学中的数学物理问题。气象出版社，北京，540页。
此书主要是介绍变分原理和稳定性理论以及这些理论在流体力学及大气动力学中的应用。全书内容详实、可读性强，高度推荐！