Abstract
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 Hs(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.
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