Well‐posedness for the Cauchy problem of the modified Hunter–Saxton equation in the Besov spaces. (19th December 2014) - Mi, Yongsheng; Mu, Chunlai
Abstract : This paper is concerned with the Cauchy problem of the modified Hunter‐Saxton equation. The local well‐posedness of the model equation is obtained in Besov spaces B p, r s, p, r ∈ [ 1, ∞ ], s > max 3 2, 1 + 1 p (which generalize the Sobolev spaces H s ) by using Littlewood‐Paley decomposition and transport equation theory. Moreover, the local well‐posedness in critical case (with s = 3 2, p = 2, r = 1 ) is considered.