The global conservative solutions for the generalized Camassa-Holm equation
This paper deals with the continuation of solutions for the generalized Camassa-Holm equation \[ u_t-u_{txx}+\frac{(m+2)(m+1)}{2}u^mu_x=\Big(\frac{m}{2}u^{m-1}(u_x)^2+u^mu_{xx}\Big)_x, \] where \(m\) is a positive integer. They transform the previous equation to a semi-linear system using a new set of variables. Then they get the existence of global conservative solutions to the original equation by establishing the existence and uniqueness of the global solutions to the semi-linear system.
scientific article; zbMATH DE number 7189492
scientific article