On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation

Advances in Differential Equations

Volumn 2, Issue 2, 1997, Pages 257-296

  Moise, R ^a,b   Rosa, R ^a,c  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

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EID: 84894538982     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. F. Abergel, Attractors for a Navier-Stokes flow in an unbounded domain, Math. Mod. and Num. Anal., 23 (1989), 359-370.
2. F. Abergel, Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains, J. Diff. Eqs., 83 (1990), 85-108.
3. J. M. Ball, A proof of the existence of global attractors for damped semilinear wave equations, to appear.
4. J. Bona and R.S. Smith, The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London Ser. A, 278 (1975), 555-604.
5. J. M. Ghidaglia, Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time, J. Diff. Eqs., 74 (1988), 369-390.
6. J. M. Ghidaglia, A note on the strong convergence towards attractors of damped forced KdV equations, J. Diff. Eqs., 110 (1994), 356-359.
7. J. M. Ghidaglia and R. Temam, Attractors for damped nonlinear hyperbolic equations, J. Math. Pures Appl., 66 (1987), 273-319.
8. O. Goubet, Regularity of the attractor for the weakly damped nonlinear Schrödinger equation, Applicable Analysis, to appear.
9. C. E. Kenig, G. Ponce, and L. Vega, Well-posedness of the initial value problem for the Kortweg-de Vries equation, J. Amer. Math. Soc., 4 (1991), 323-347.
10. D. J. Korteweg and G. de Vries, On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary wave, Phil. Mag., 39 (1895), 422-443.
11. M. D. Kruskal, R. M. Miura, C. S. Gardner, and N. J. Zabusky, Korteweg-de Vries equation and generalizations V. Uniqueness and nonexistence of polynomial conservation laws, J. Math. Phys., 11 (1970), 952-960.
12. O. Ladyzhenskaya, "Attractors for Semigroups and Evolution Equations," Lezioni Lincei, Cambridge University Press, 1991.
13. R. M. Miura, C. S. Gardner, and M. D. Kruskal, Kortweg-de Vries equation and generalizations II. Existence of conservation laws and constants of motion, J. Math. Phys., 9(1968),1204-1209.
14. A. C. Newell, Solitons in Mathematics and Physics, volume 48 of CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1985.
15. E. Ott and R. N. Sudan, Damping of solitary waves, Phys. Fluids, 13 (1970), 1432-1434.
16. R. Rosa, The global attractor for the 2D Navier-Stokes flow on some unbounded domains, submitted.
17. J. C. Saut and R. Temam, Remarks on the Korteweg-de Vries equation, Israel J. Math., 24 (1976), 78-87.
18. R. Temam, Sur un probleme non-linéaire, J. Math. Pures Appl., 48 (1969), 159-172.
19. R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Springer-Verlag, New York, 1988.
20. M. Tsutsumi and T. Mukasa, Parabolic regularizations for the generalized Korteweg-de Vries equation, Funkcialaj Ekvacioj, 14 (1971), 89-110.
21. X. Wang, An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications to their attractors, to appear.