Continuity and analyticity for a generalized two-component short pulse system

In this paper, we first established the local well-posedness of the generalized short pulse system in the critical Besov space $B_{2,1}^{\frac{3}{2}}(\mathbb{T})$, improving upon the local well-posedness result obtained in [S. Yu, X. Yin, J. Math. Anal. Appl., 475 (2019), 1427–1447]. We then proved that the solution map was Hölder continuous in $B_{2,r}^{\mu }(\mathbb{T})$. Finally, by a generalized Ovsyannikov theorem combined with fundamental properties of Sobolev-Gevrey spaces, we established the Gevrey regularity and analyticity of solutions and further obtained a lower bound of the lifespan and the continuity of the data-to-solution map.