Gene

Camassa–Holm equation

Initial value problem

Hadamard transform

Pure mathematics

Functional analysis

Interpolation space

Applied mathematics

Cauchy problem

Biochemistry

Besov space

Geology

Paleontology

Type (biology)

Integrable system

Mathematics

Mathematical analysis

Chemistry

Journal of Differential Equations

In this paper, we prove the solution map of the Cauchy problem of Camassa–Holm type equations depends continuously on the initial data in nonhomogeneous Besov spaces in the sense of Hadamard by using the Littlewood–Paley theory and the method introduced by Kato [37] and Danchin [21].

Remarks on the well-posedness of Camassa–Holm type equations in Besov spaces