Local well-posedness and blow-up phenomena of the generalized short pulse equation.

In this paper, we investigate the Cauchy problem of the generalized short-pulse equation in periodic domain. We first establish the local well-posedness of the equation in H s (S) , s ≥ 2 by taking advantage of the Kato method and present some useful conservation laws. Then, we obtain the boundedness of the solution by virtue of the conservation laws. Finally, we give a precise blow-up criterion for α > 0 (or α < 0) and get several blow-up results provided the initial data satisfies some certain conditions. [ABSTRACT FROM AUTHOR]