The <em>C<sup>k</sup></em> Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions

HE You-hua; SHI Wei-hui

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HE You-hua, SHI Wei-hui. The Ck Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1301-1309.

Citation:

HE You-hua, SHI Wei-hui. The C^k Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1301-1309.

HE You-hua, SHI Wei-hui. The Ck Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1301-1309.

Citation:

HE You-hua, SHI Wei-hui. The C^k Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1301-1309.

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The C^k Instability of Navier-Stokes Equation Appending Polynomials of Unknown Functions

Department of Mathematics, Shanghai University, Shanghai 210800, P R China

Received Date: 2000-03-15
Rev Recd Date: 2000-07-20
Publish Date: 2000-12-15

Abstract

Abstract

Applying the theory of stratification,the solution space structure about a class of deformed Navier-Stokes equation is determined.It is proved that such kind of equation has no C^k(k≥2)stable solution by the fact that the strate transversale is a null set.
- Navier-Stokes equation,
- unstable equation,
- strate transversale

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References(9)

References

[1]	Landau L, Lifchitz E. Mécaniquedes Fluides [M]. Moscou: Mir,1971.
[2]	Ride H. On planetary atmospheres and interiors[J]. Mathematical in the Geophysical Science, Amer Math Soc, Providence R I,1971.
[3]	唐一呜. 磁通量方程的解空间构造[A]. 见:戴世强主编.现代数学与力学,MMM-Ⅶ[C]. 上海:上海大学出版社,1997,445-452.
[4]	SHIH Wei-hui. Solutions Analytiques de Quelques ^*quations aux D érivées Partiellesen Mécanique des Fluides[M]. Paris: Hermann,1992.
[5]	SHIH Wei-shu. Une remarque surles systèmes d'équations aux dé rivées partielles analytiques réelles Ⅱ[J]. C R Acad Sci Paris, Série Ⅰ,1987,304(4):103-106.
[6]	SHIH Wei-shu. Une methode élémentaire pour l'étude des équations auxdérivées partielles[J]. Diagrammes,Paris,1986,(16):1-89.
[7]	Trotmann D, Wilsom L. Singularities of Maps and Applications to Differential Equations[M]. Paris: Hermann,1997.
[8]	陈达段,刘晓明,施惟慧. 关于强迫耗散非线性系统的稳定性[J]. 应用数学和力学,1996,17(6):515-522.
[9]	SHIH Wei-hui, CHEN Da-duan. On the instability of incompressible Helium-Ⅱ complete equation[A]. In: CHIEN Wei-zang Ed.ICNM-Third International Conference on Nonlinear Mechanics[C]. Shanghai: Shanghai University Press,1998,848-853.