On the global existence and wave-breaking criteria for the two-component Camassa-Holm system

By Guilong Gui, Yue Liu. 2010

277 citations recorded by the source corpus.

Considered herein is a two-component Camassa–Holm system modeling shallow water waves moving over a linear shear flow. A wave-breaking criterion for strong solutions is determined in the lowest Sobolev space Hs, s>32 by using the localization analysis in the transport equation theory. Moreover, an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this Sobolev space Hs.

Subfields: Mathematical Physics, Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63cba4c0b1d6f00a5e01cfa8d236f863b76d827a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Robin Ming Chen
2. Yue Liu
3. Zhaoyang Yin
4. Changzheng Qu
5. Ying Fu

In Oceanography

1. Robin Ming Chen
2. Yue Liu

In Statistical and Nonlinear Physics

1. Robin Ming Chen
2. Yue Liu
3. Zhaoyang Yin
4. Changzheng Qu
5. Ying Fu

Citations in the corpus

• Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, unknown): “(See [2,24].”
• Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, methodology): “This blow-up criterion is further improved in [30] to the lowest Sobolev spaces Hs(R)×Hs−1(R) with s > 3/2.”