Unconditional local well-posedness for periodic NLS

2019/12/29 by Nobu Kishimoto, Kishimoto, Nobu · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1912.12704

openalex publication_date 2019/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The nonlinear Schrödinger equations with nonlinearities |u|^2ku on the d-dimensional torus are considered for arbitrary positive integers k and d. The solution of the Cauchy problem is shown to be unique in the class C_tH^s_x for a certain range of scale-subcritical regularities s, which is almost optimal in the case d≥ 4 or k≥ 2. The proof is based on various multilinear estimates and the infinite normal form reduction argument.

Citations

• Multilinear estimates for periodic KdV equations, and applications

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• Sharp unconditional well-posedness of the 2-d periodic cubic hyperbolic nonlinear Schrödinger equation
• Nonlinear PDEs with modulated dispersion IV: normal form approach and unconditional uniqueness

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