Local and global analyticity for \(\mu\)-Camassa-Holm equations (Q2176545)

This paper deals with the \(\mu\)-Camassa-Holm equations \[ \mu(u_t) - u_{txx} = -2\mu(u)u_x + 2u_xu_{xx} + uu_{xxx}, \quad x \in \mathbb{S}^1= \mathbb{R}/\mathbb{Z}, \] where \[ \mu(u) =\int_{\mathbb{S}^1}u dx. \] The author proves the unique local solvability of the Cauchy problem, provide an estimate of the lifespan of the solutions, and the existence of a unique global-in-time analytic solution.