# American Institute of Mathematical Sciences

August  2013, 33(8): 3407-3441. doi: 10.3934/dcds.2013.33.3407

## On the Cauchy problem for the two-component Dullin-Gottwald-Holm system

 1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China 2 Jiangsu Key Laboratory for NSLSCS and School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China 3 Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408

Received  May 2012 Revised  October 2012 Published  January 2013

Considered herein is the initial-value problem for a two-component Dullin-Gottwald-Holm system. The local well-posedness in the Sobolev space $H^{s}(\mathbb{R})$ with $s>3/2$ is established by using the bi-linear estimate technique to the approximate solutions. Then the wave-breaking criteria and global solutions are determined in $H^s(\mathbb{R}), s > 3/2.$ Finally, existence of the solitary-wave solutions is demonstrated.
Citation: Yong Chen, Hongjun Gao, Yue Liu. On the Cauchy problem for the two-component Dullin-Gottwald-Holm system. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3407-3441. doi: 10.3934/dcds.2013.33.3407
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