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

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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 Hirota-Satsuma system.

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. A.P. is partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brasil (CNPq) grant 2019/02512-5.

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  1. IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brazil

    Alexander Muñoz & Ademir Pastor

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  1. Alexander Muñoz
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  2. Ademir Pastor
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Correspondence to Ademir Pastor.

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Communicated by Roseline Periyanayagam.

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Muñoz, A., Pastor, A. Local well-posedness in weighted Sobolev spaces for nonlinear dispersive equations with applications to dispersive blow up. Math. Ann. 386, 207–246 (2023). https://doi.org/10.1007/s00208-022-02396-7

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  • DOI: https://doi.org/10.1007/s00208-022-02396-7

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