The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)

摘要

The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C ( [ 0 , ∞ ) × R ) ∩ L ∞ ( [ 0 , ∞ ) ; H 1 ( R ) ) under the assumption that the initial value u 0 ( x ) only belongs to the space H 1 ( R ) . 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.