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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 327572, 15 pages
http://dx.doi.org/10.1155/2012/327572
Research Article

On the Global Well-Posedness of the Viscous Two-Component Camassa-Holm System

School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China

Received 3 January 2012; Accepted 15 February 2012

Academic Editor: Valery Covachev

Copyright © 2012 Xiuming Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Constantin and R. I. Ivanov, “On an integrable two-component Camassa-Holm shallow water system,” Physics Letters A, vol. 372, no. 48, pp. 7129–7132, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. P. J. Olver and P. Rosenau, “Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support,” Physical Review E, vol. 53, no. 2, pp. 1900–1906, 1996. View at Publisher · View at Google Scholar
  3. R. Ivanov, “Two-component integrable systems modelling shallow water waves: the constant vorticity case,” Wave Motion, vol. 46, no. 6, pp. 389–396, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. A. Constantin and W. Strauss, “Exact steady periodic water waves with vorticity,” Communications on Pure and Applied Mathematics, vol. 57, no. 4, pp. 481–527, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. S. Johnson, “Nonlinear gravity waves on the surface of an arbitrary shear flow with variable depth,” in Nonlinear Instability Analysis, vol. 12 of Adv. Fluid Mech., pp. 221–243, Comput. Mech., Southampton, UK, 1997.
  6. R. S. Johnson, “On solutions of the Burns condition (which determines the speed of propagation of linear long waves on a shear flow with or without a critical layer),” Geophysical and Astrophysical Fluid Dynamics, vol. 57, no. 1–4, pp. 115–133, 1991. View at Publisher · View at Google Scholar
  7. P. Popivanov and A. Slavova, Nonlinear Waves, vol. 4 of Series on Analysis, Applications and Computation, World Scientific, Hackensack, NJ, USA, 2011.
  8. M. Chen, S.-Q. Liu, and Y. Zhang, “A two-component generalization of the Camassa-Holm equation and its solutions,” Letters in Mathematical Physics, vol. 75, no. 1, pp. 1–15, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. D. D. Holm, L. Nraigh, and C. Tronci, “Singular solutions of a modified two-component Camassa-Holm equation,” Physical Review E, vol. 85, no. 1, Article ID 016601, 5 pages, 2012. View at Publisher · View at Google Scholar
  10. J. Escher, O. Lechtenfeld, and Z. Yin, “Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation,” Discrete and Continuous Dynamical Systems. Series A, vol. 19, no. 3, pp. 493–513, 2007. View at Zentralblatt MATH
  11. G. Gui and Y. Liu, “On the Cauchy problem for the two-component Camassa-Holm system,” Mathematische Zeitschrift, vol. 268, no. 1-2, pp. 45–66, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. Gui and Y. Liu, “On the global existence and wave-breaking criteria for the two-component Camassa-Holm system,” Journal of Functional Analysis, vol. 258, no. 12, pp. 4251–4278, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. W. K. Lim, “Global well-posedness for the viscous Camassa-Holm equation,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 432–442, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH