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arXiv · 2112.12734

Strichartz and Multi-linear Estimates for the One-dimensional Periodic Dysthe equation

Garrett Heller·Chengyang Shao
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Abstract

This paper presents Strichartz estimates for the linearized 1D periodic Dysthe equation on the torus, namely estimate of the $L^6_{x,t}(\mathbb{T}^2)$ norm of the solution in terms of the initial data, and estimate of the $L^4_{x,t}(\mathbb{T}^2)$ norm in terms of the Bourgain space norm. The paper also presents other results such as bilinear and trilinear estimates pertaining to local well-posedness of the 1-dimensional periodic Dysthe equation in a suitable Bourgain space, and ill-posedness results in Sobolev spaces.

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Garrett Heller, Chengyang Shao. 2021-12-17. Strichartz and Multi-linear Estimates for the One-dimensional Periodic Dysthe equation. https://arxiv.org/abs/2112.12734

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