Time dependent periodic Navier-Stokes flows on a two-dimensional torus

Communications in Mathematical Physics

Volumn 179, Issue 3, 1996, Pages 577-597

  Chen, Zhi Min ^a   Price, W G ^b  

^a TIANJIN UNIVERSITY   (China)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030240542     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02100098     Document Type: Article

References (18)

1. Arnold, V. I., Meshalkin, L. D.: A. N. Kolmogorov's seminar on selected problems of analysis (1958-1959). Russ. Math. Surv. 15 (1), 247-250 (1960)
2. Franceschini, V., Giberti, C., Nicolini, M.: Common periodic behaviour in larger truncations of the Navier-Stokes equations. J. Stat. Phys. 50, 879-896 (1988)
3. Guckenheimer, J., Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Berlin: Springer, 1983
4. Iudovich, V. I.: Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid. J. Math. Mech. 29(4), 587-603 (1965)
5. Iudovich, V. I.: The onset to auto-oscillations in a fluid. J. Math. Mech. 35(3), 453-467 (1971)
6. Lambert, J. D.: Numerical methods for ordinary differential systems. Chichester: Wiley, 1991
7. Landau, L.: On the problem of turbulence. Comptes Rend. Acad. Sci. USSR 44, 311-316 (1944)
8. Liu, V. X.: An example of instability for the Navier-Stokes equations on the 2-dimensional torus. Commun. Partial Differential Eqs. 17, 1995-2012 (1992a)
9. Liu, V. X.: Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the Hausdorff dimension of their global attractors. Commun. Math. Phys. 147, 217-230 (1992b)
10. Marchioro, C.: An example of absence of turbulence for any Reynolds number. Commun. Math. Phys. 105, 99-106 (1986)
11. Marsden, J. E., McCracken, M.: The Hopf bifurcation and its applications. Berlin: Springer, 1976
12. Massey, M. S.: A basic course in algebraic topology. Berlin: Springer, 1991
13. Meshalkin, L. D., Sinai, Ya. G.: Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous fluid. J. Math. Mech. 19(9), 1700-1705 (1961)
14. n, n ≥ 3. Commun. Math. Phys. 64, 35-40 (1978)
15. Okamoto, H., Shoji, M.: Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori. Kyoto Univ. Res. Inst. Math. Sci. 767, 29-51 (1991)
16. Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys. 20, 167-192 (1971)
17. Thompson, J. M. T., Stewart H. B.: Nonlinear dynamics and chaos. Chichester: Wiley, 1986
18. Triebel, H.: Interpolation theory, function spaces, differential operators. Amsterdam: North-Holland, 1978