On the Backwards Behavior of the Solutions of the 2D Periodic Viscous Camassa-Holm Equations

Journal of Dynamics and Differential Equations

Volumn 14, Issue 1, 2002, Pages 37-62

  Vukadinović, Jesenko ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Global solutions; Viscous Camassa Holm equations; Voracity quotients

Indexed keywords

EID: 0242436671     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1012963327420     Document Type: Article

References (16)

1. Bardos, C., and Tartar, L. (1973). Sur l'unicité rétrograde des équations paraboliques et queliques questions voisines. Arch. Rational Mech. Anal. 50, 10-25.
2. Camassa, R., and Holm, D. D. (1993). A completely integrable dispersive shallow water equation with peaked solutions. Phys. Rev. Lett. 71, 1661-1664.
3. Camassa, R., Holm, D. D., and Hyman, J. M. (1994). A new integrable shallow water equation with peaked solutions. Adv. Appl. Mech. 31, 1-33.
4. Chen, S., Foias, C., Holm, D. D., Olson, E., Titi, E. S., and Wynn, S. (1998). A connection between the Camassa-Holm equations and turbulent flows in channels and pipes. Phys. Fluids 11, 2343-2353.
5. Constantin, A., and Foias, C. (1988). Navier-Stokes Equations, Chicago Lectures in Mathematics, Chicago/London.
6. Constantin, A., Foias, C., Kukavica, I., and Majda, A. J. (1997). Dirichlet quotients and 2D periodic Navier-Stokes equations. J. Math. Pures Appl. 76, 125-153.
7. Constantin, A., Foias, C., and Temam, R. (1988). On the dimension of attractors in twodimensional turbulence. Physica D 30, 284-296.
8. Doering, C., Gibbon, J. D., Holm, D., and Nicolaenko, B. (1988). Low-dimensional behavior in the complex Ginzburg-Landau equation. Nonlinearity 1, 279-309.
9. Foias, C., and Kukavica, I., private communications.
10. Foias, C., and Saut, J. C. (1981). Limite du rapport de l'enstrophie sur l'énergie pour une solution faible des équations de Navier-Stokes. C. R. Acad. Sci. Paris, Sér. I Math. 298, 241-244.
11. Foias, C., and Saut, J. C. (1984). Asymptotic behavior, as t → ∞, of solutions of Navier-Stokes equations and nonlinear spectral manifolds. Indiana Univ. Math. J. 33, 459-4177.
12. Foias, C., Sell, G. R., and Temam, R. (1988). Inertial manifolds for nonlinear evolutionary equations. J. Diff. Eq. 73, 309-353.
13. Holm, D. D., Marsden, J. E., and Ratiu, T. S. (1998). Euler-Poincaré models of ideal fluids with nonlinear dispersion. Phys. Rev. Lett. 80, 4173.
14. Holm, D. D., Marsden, J. E., and Ratiu, T. S. (1998). Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math. 137, 1.
15. Kukavica, I. (1992). On the behavior of the Solutions of the Kuramoto-Sivashinsky Equations for negative time. J. Math. Anal. Appl. 166, 601-606.
16. Temam, R. (1984). Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam.