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arXiv · 2504.09333

Global results for weakly dispersive KP-II equations on the cylinder

Sebastian Herr·Robert Schippa·Nikolay Tzvetkov
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Abstract

We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these at hand, we show global well-posedness of the quasilinear Cauchy problem in $L^2(\mathbb{R} \times \mathbb{T})$. Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.

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Sebastian Herr, Robert Schippa, Nikolay Tzvetkov. 2025-04-12. Global results for weakly dispersive KP-II equations on the cylinder. https://arxiv.org/abs/2504.09333

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