A blow-up result for the periodic Camassa-Holm equation

Archiv der Mathematik

Volumn 84, Issue 4, 2005, Pages 334-340

  Wahlén, Erik ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18244365592     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-004-1199-4     Document Type: Article

References (21)

1. R. CAMASSA and D. HOLM, An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664 (1993).
2. A. CONSTANTIN, On the Cauchy problem for the periodic Camassa-Holm equation. J. Differential Equ. 141, 218-235 (1997).
3. A. CONSTANTIN and J. ESCHER, Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 181, 229-243 (1998).
4. A. CONSTANTIN and I. ESCHER, Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math. 51, 475-504 (1998).
5. A. CONSTANTIN and J. ESCHER, On the structure of a family of quasilinear equations arising in shallow water theory. Math. Ann. 312, 403-416 (1998).
6. A. CONSTANTIN and J. ESCHER, On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Math. Z. 233, 75-91 (2000).
7. A. CONSTANTIN and B. KOLEV, On the geometric approach to the motion of inertial mechanical systems. J. Phys. A 35, R51-R79 (2002).
8. A. CONSTANTIN and B. KOLEV, Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78, 787-804 (2003).
9. A. CONSTANTIN and H. P. MCKEAN, A shallow water equation on the circle. Comm. Pure Appl. Math. 52, 949-982 (1999).
10. A. CONSTANTIN and L. MOLINET, Global weak solutions for a shallow water equation. Comm. Math. Phys. 211, 45-61 (2000).
11. A. CONSTANTIN and W. STRAUSS, Stability of peakons. Comm. Pure Appl. Math. 53, 603-610 (2000).
12. A. FOKAS and B. FUCHSSTEINER, Symplectic structures, their Backlund transformation and hereditary symmetries. Physica D 4, 47-66 (1981/1982).
13. R. S. JOHNSON, Camassa-Holm, Korteweg-de Vries and related models for water waves. J. Fluid. Mech. 455, 63-82 (2002).
14. J. LENELLS, Stability of periodic peakons. Int. Math. Res. Not. 2004, 485-499 (2004).
15. J. LENELLS, A variational approach to the stability of periodic peakons. J. Nonlinear Math. Phys. 11, 151-163 (2004).
16. Y. A. LI and P. J. OLVER, Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equ. 162, 27-63 (2000).
17. G. MISIOLEK, A shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys. 24, 203-208 (1998).
18. E. WAHLÉN, On the blow-up of solutions to the periodic Camassa-Holm equation. NoDEA. To appear.
19. Z. YIN, On the blow-up of solutions of the periodic Camassa-Holm equation. Dyn. Cont Dis. Impul. Syst. To appear.
20. Y. ZHOU, Wave breaking for a periodic shallow water equation. I. Math. Anal. Appl. 290, 591-604 (2004).
21. Y. ZHOU, A remark on blowup of solutions to the periodic Camassa-Holm equation. J. Math. Anal. Appl. To appear.