Mathematische Annalen

, Volume 335, Issue 3, pp 717–735

Global existence and blow-up solutions for a nonlinear shallow water equation


DOI: 10.1007/s00208-006-0768-1

Cite this article as:
Liu, Y. Math. Ann. (2006) 335: 717. doi:10.1007/s00208-006-0768-1


Considered herein are the problems of the existence of global solutions and the formation of singularities for a new nonlinear shallow water wave equation derived by Dullin, Gottward and Holm. Blow-up can occur only in the form of wave-breaking. A wave-breaking mechanism for solutions with certain initial profiles is described in detail and the exact blow-up rate is established. The blow-up set for a class of initial profiles and lower bounds of the existence time of the solution are also determined.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TexasArlington