The study on solutions to Camassa-Holm equation with weak dissipation

Communications on Pure and Applied Analysis

Volumn 5, Issue 3, 2006, Pages 483-492

  Ding, Danping ^a   Tian, Lixin ^a   Xu, Gang ^a  

^a JIANGSU UNIVERSITY   (China)

Author keywords

Blow up; Solitary; Weak dissipation Camassa Holm equation

Indexed keywords

EID: 33749425690     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2006.5.483     Document Type: Article

References (15)

1. R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys.Rev.Lett., 71 (1993), 1661-1664.
2. S. Chen, C. Foias and D.D. Holm, The Camassa-Holm equations as a closure model for turbulent channel flow, Phys.Rev.Lett., 81 (1998), 5338-5342.
3. C. Foias, D. Holm and S. Titi, The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. Journal of Dynamics and Differential Equations, 14 (2002), 1-35.
4. J. Vukadinovic, On the backwards behavior of the solutions of the 2D periodic viscous Camassa-Holm equation. Journal of Dynamics and Differential Equations, 14 (2002), 37-62.
5. R. Temam, Infinite dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, Springer-Verlag, Berlin, 68 (1988).
6. T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equations.in: studies in Applied Mathematic,Advances in Mathematics, supplementarystudies, Academic press. New York-London, 8 (1983), 93-128.
7. T. Kato, Quasilinear equations of evolution, with application to partial differential equations. in: spectral theory and differential equations: Proceedings of the symposium Held at Dundee, Scotland, 1-19 (1974), 25-79.
8. A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Ann. Scuola Norm, SUP.Pisacl.Sci., 26 (1998), 303-328.
9. A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equation, Acta Mathematica, 181 (1998), 229-243.
10. A. Constantin and J. Escher, Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation, Communications on Pure and Applied Mathematics, 11 (1998), 0475-0504.
11. A. Constantin and L. Molinet, Global weak solutions for a shallow water equation, Commun. Math. Phys., 211 (2000), 45-61.
12. Guo Boling, Infinite Dimensional Dynamical Systems, Defense industry Press, Beijing, 2000.
13. Xinmin Xiang, The Long-time Behavior For Nonlinear Schroodinger Equation And Its Rational Pseudospectral Approximation, Discrete And Continuous Dynamical Systems-Series B, 5 (2005), 469-488.
14. Juan-Ming Yuan and Jiahong Wu, The Complex KdV Equation With Or Without Dissipation, Discrete And Continuous Dynamical Systems-Series B, 5 (2005), 489-512.
15. Lixin Tian, WAIM in nonlinear solitary wave equation, J. Math. Phy., 41 (2000), 5773-5793.