The Global Weak Solution for a Generalized Camassa-Holm Equation

Abstract EN

A nonlinear generalization of the famous Camassa-Holm model is investigated.

Provided that initial value u0∈Hs(R)(1≤s≤3/2) and (1-∂x2)u0 satisfies an associated sign condition, it is shown that there exists a unique global weak solution to the equation in space u(t,x)∈L2([0,+∞),Hs(R)) in the sense of distribution, and ux∈L∞([0,+∞)×R).