J4 ›› 2011, Vol. 46 ›› Issue (2): 34-38.

• Articles • Previous Articles     Next Articles

Large time behavior for a simplified 1d viscous Camassa-Holm equation model of fluid-solid interaction

ZONG Xi-ju, WANG Zhong-hua   

  1. School of Control Science and Engineering, University of Jinan, Jinan 250022,  Shandong, China
  • Received:2008-06-28 Online:2011-02-16 Published:2011-03-30


A simple model in one space dimension for the interaction between a fluid and a solid represented by a point mass is considered. By using the semi-group theorem and Banach fixed-point theorem,  the existence and uniqueness of the solution to the system is proved. Furthermore,  the asymptotic behavior of solutions for integrable data using energy estimates is described. That asymptotically the difference of pressure to both sides of the point mass vanishes is also proved.

Key words: one-dimension viscous Camassa-Holm equation; fluid-Solid Interaction; Banach fixed-point theorem; energy estimate

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