On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation

Details On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation

2011-07-16

arxiv.org/abs/1107.3191v2

Mathematics

Analysis of PDEs

31 pages

Scientific paper

Considered herein is the initial-value problem for the generalized periodic Camassa-Holm equation which is related to the Camassa-Holm equation and the Hunter-Saxton equation. Sufficient conditions guaranteeing the development of breaking waves in finite time are demonstrated. On the other hand, the existence of strong permanent waves is established with certain initial profiles depending on the linear dispersive parameter in a range of the Sobolev spaces. Moreover, the admissible global weak solution in the energy space is obtained.

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