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arXiv · 2510.00692

Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system

Hung Luong
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Abstract

In this paper, we revisit the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. Our method is based on the dispersive estimates and the suitable Bourgain's spaces. We then, obtain the local well-posedness of the solution with the main component $\psi$ belongs to $H^1(\mathbb{R}^d)$ ($d=2, 3$) which is actually the energy space corresponding to this component. Our result also suggests a potential approach to the problem of finding exact existence time scale for the solution of Benney-Roskes model in the context of water waves.

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Hung Luong. 2025-10-01. Revisiting the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. https://arxiv.org/abs/2510.00692

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