The existence of global weak solutions to the Cauchy problem for a generalized Camassa-Holm equation with a dissipative term is investigated in the space × ; provided that its initial value belongs to the space . A one-sided super bound estimate and a space-time higher-norm estimate on the first-order derivatives of the solution with respect to the space variable are derived.
Zhaowei Sheng. Shaoyong Lai. Yuan Ma. Xuanjun Luo. "The Space Global Weak Solutions to the Weakly Dissipative Camassa-Holm Equation." Abstr. Appl. Anal. 2012 (SI06) 1 - 21, 2012. https://doi.org/10.1155/2012/693010