Small data global well--posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in H^s (\mathbb Rⁿ)

2021/07/02 by JinMyong An, An, JinMyong, JinMyong Kim +1
Mathematics · Physics and Astronomy · #2020 MSC: 35Q55 #35A01 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2107.00792

openalex publication_date 2021/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger (INLS) equation iu_t +Δu=|x|^-b f(u), u(0)=u₀ ∈ H^s (\mathbb Rⁿ), where 00. We prove that the Cauchy problem of the INLS equation is globally well--posed in H^s (\mathbb Rⁿ) if the initial data is sufficiently small and σ₀

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