Large data scattering for the defocusing supercritical generalized KdV equation

Luiz G. Farah; Felipe Linares; Ademir Pastor; Nicola Visciglia

doi:10.1080/03605302.2018.1439063

Large data scattering for the defocusing supercritical generalized KdV equation

Analysis of PDEs 2021-08-26 v1

Authors: Luiz G. Farah , Felipe Linares , Ademir Pastor , Nicola Visciglia

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Abstract

We consider the defocusing supercritical generalized Korteweg-de Vries (gKdV) equation $\partial_t u+\partial_x^3u-\partial_x(u^{k+1})=0$ , where $k>4$ is an even integer number. We show that if the initial data $u_0$ belongs to $H^1$ then the corresponding solution is global and scatters in $H^1$ . Our method of proof is inspired on the compactness method introduced by C. Kenig and F. Merle.

Cite

@article{arxiv.1707.03455,
  title  = {Large data scattering for the defocusing supercritical generalized KdV equation},
  author = {Luiz G. Farah and Felipe Linares and Ademir Pastor and Nicola Visciglia},
  journal= {arXiv preprint arXiv:1707.03455},
  year   = {2021}
}

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36 pages

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