In the present paper, we use some standard a priori estimates for linear transport equations to prove the existence and uniqueness of solutions for the Camassa-Holm equation with minimal regularity assumptions on the initial data. We also derive some explosion criteria and a sharp estimate from below for the existence time. We finally address the question of global existence for certain initial data. This yields, among other things, a different proof for the existence and uniqueness of Constantin and Molinet's global weak solutions (see ).
Raphaël Danchin. "A few remarks on the Camassa-Holm equation." Differential Integral Equations 14 (8) 953 - 988, 2001. https://doi.org/10.57262/die/1356123175