The Cauchy problem for generalized fractional Camassa–Holm equation in Besov space

Abstract

Consideration in this paper is the generalized fractional Camassa–Holm equation. The local well-posedness is established in Besov space $$B^{s_0}_{2,1}$$ with $$s_0=2\nu -\frac{1}{2}$$ for $$\nu >\frac{3}{2} $$ and $$s_0=\frac{5}{2}$$ for $$1<\nu \le \frac{3}{2} $$ . Then, with a given analytic initial data, the analyticity of the solutions in both variables, globally in space and locally in time, is established. Finally, a blow-up criterion is presented.