Phase turbulence in the Complex Ginzburg-Landau equation via Kuramoto-Sivashinsky phase dynamics

Communications in Mathematical Physics

Volumn 247, Issue 3, 2004, Pages 613-654

  Van Baalen, Guillaume ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2942741073     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1073-z     Document Type: Article

References (12)

1. [BKL94] Bricmont, J., Kupiainen, A., Lin, G.: Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations. Commun. Pure Appl. Math. 47(6), 893-922 (1994)
2. [GvB02] van Baalen, G.: Stationary solutions of the Navier-Stokes equations in a half-plane down-stream of an obstacle: 'universality' of the wake. Nonlinearity 15(2), 315-366 (2002)
3. [CH93] Cross, M., Hohenberg, P.: Rev. Mod. Phys. 65, 851 (1993)
4. [CEES93] Collet, P., Eckmann, J.-P., Epstein, H., Stubbe, J.: A global attracting set for the Kuramoto-Sivashinsky equation. Commun. Math. Phys. 152(1), 203-214 (1993)
5. [KT76] Kuramoto, Y., Tsuzuki, T.: Persistent Propagation of Concentration Waves in Dissipative Media Far from Thermal Equilibrium. Prog. Theor. Phys. 55, 356-369 (1976)
6. [EGW95] Eckmann, J.-P., Gallay, Th., Wayne, C.E.: Phase slips and the Eckhaus instability. Nonlinearity 8(6), 943-961 (1995)
7. [Man90] Manneville, P.: Dissipative structures and weak turbulence. Boston, MA: Academic Press, 1990
8. [MHAM97] Montagne, R., Hernández-García, E., Amengual, A., San Miguel, M.: Wound-up phase turbulence in the complex Ginzburg-Landau equation. Phys. Rev. E (3) 56(1 ), part A, 151-167 (1997)
9. [New74] Newell, A.: Lect. Appl. Math. 15, 157 (1974)
10. [NST85] Nicolaenko, B., Scheurer, B., Temam, R.: Phys. D 16(2), 155-183 (1985)
11. [Tem97] Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics. Second edition, New York: Springer, 1997
12. [BF67] Benjamin, T.B., Feir, J.: J. Fluid Mech. 27, 417 (1967)