The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in
1 Department of Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China
2 Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia
Boundary Value Problems 2013, 2013:26 doi:10.1186/1687-2770-2013-26Published: 12 February 2013
The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space under the assumption that the initial value only belongs to the space . The limit of viscous approximations, a one-sided super bound estimate and a space-time higher-norm estimate for the equation are established to prove the existence of the global weak solution.
MSC: 35G25, 35L05.