In the first part of this work we study the local well-posedness of dispersive equations in the weighted spaces $H^s(\mathbb{ R})\cap L^2(|x|^{ 2b}dx)$. We then apply our results for several dispersive models such as the Hirota-Satsuma system, the OST equation, the Kawahara equation and a fifth-order model. Using these local results, the second part of this work is devoted to obtain results related to dispersive blow up of the Kawahara equation and the Hirota-Satsuma system.
Categories: math.AP