The support of the momentum density of the Camassa–Holm equation

Bounds for the size of the support of a compactly supported momentum density of the Camassa–Holm equation are derived. This is achieved by estimating the first Dirichlet eigenvalue of the support. This elaborates the result on the preservation of its compactness, and gives more information on the velocity by estimating the size of the region where it is not that well understood.