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arXiv · 1707.03455

Large data scattering for the defocusing supercritical generalized KdV equation

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.

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Luiz G. Farah, Felipe Linares, Ademir Pastor, Nicola Visciglia. 2017-07-11. Large data scattering for the defocusing supercritical generalized KdV equation. https://doi.org/10.1080/03605302.2018.1439063

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