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

2021/12/17 by Garrett Heller, Heller, Garrett, Chengyang Shao +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.12734

openalex publication_date 2021/12/17 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

This paper presents Strichartz estimates for the linearized 1D periodic Dysthe equation on the torus, namely estimate of the L⁶_x,t(\mathbbT²) norm of the solution in terms of the initial data, and estimate of the L⁴_x,t(\mathbbT²) 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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