Well-posedness for a modified two-component Camassa-Holm system in critical spaces
The authors address local solutions of a two-component generalization of the Camassa-Holm equation. They work in Besov spaces with the critical index \(s = 3/2\). The results can be extended from the case of real line to the case of the periodic domain. The paper consists of three sections. After an introduction, the authors review the construction of Besov spaces, Littlewood-Paley decomposition, and other basic inequalities. In the main Section 3, the authors prove the main result, which guarantees a local well-posedness of the solutions of the two-component Camassa-Holm system in critical Besov spaces. The analysis is based on modified Kato-Picard iterations for quasilinear dispersive wave equations.
scientific article; zbMATH DE number 6157274