Several Dynamic Properties of Solutions to a Generalized Camassa-Holm Equation

Abstract

For a nonlinear generalization of the Camassa-Holm equation, we investigate the dynamic properties of solutions for the equation under the assumption that the initial value $u_0(x)$ lies in the space $H^1(R)$. A one-sided upper bound estimate on the first-order spatial derivative, $L^p$ bound estimate, and a space-time higher-norm estimate for the solutions are obtained.