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arXiv · 2109.08727

Local well-posedness in weighted Sobolev spaces for nonlinear dispersive equations with applications to dispersive blow up

Alexander Muñoz·Ademir Pastor
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Abstract

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.

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Alexander Muñoz, Ademir Pastor. 2021-09-17. Local well-posedness in weighted Sobolev spaces for nonlinear dispersive equations with applications to dispersive blow up. https://arxiv.org/abs/2109.08727

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