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arXiv · 2510.01728

On dispersive decay for the generalized Korteweg--de Vries equation

Matthew Kowalski·Minjie Shan
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Abstract

We prove pointwise-in-time dispersive estimates for solutions to the generalized Korteweg--de Vries (gKdV) equation. In particular, for solutions to the mass-critical model, we assume only that initial data lie in $\dot{H}^{\frac{1}{4}} \cap \dot{H}^{-\frac{1}{12}}$ and show that solutions decay in $L^\infty$ like $|t|^{-\frac{1}{3}}$. To accomplish this, we develop a persistence of negative regularity for solutions to gKdV and extend Lorentz--Strichartz estimates to the mixed norm case.

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Matthew Kowalski, Minjie Shan. 2025-10-02. On dispersive decay for the generalized Korteweg--de Vries equation. https://arxiv.org/abs/2510.01728

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