Low-regularity global solution of the inhomogeneous nonlinear Schrödinger equations in modulation spaces

2024/10/01 by Divyang G. Bhimani, Bhimani, Divyang G., Diksha Dhingra +3
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2410.00869

openalex publication_date 2024/10/01 · openalex created_date 2024/10/29 · openalex updated_date 2026/07/28

Abstract

The study of low regularity Cauchy data for nonlinear dispersive PDEs has successfully been achieved using modulation spaces M^p,q in recent years. In this paper, we study the inhomogeneous nonlinear Schrödinger equation (INLS) iu_t + Δu± |x|^-b|u|^αu=0, where α, b>0, on whole space \mathbb Rⁿ in modulation spaces. In the subcritical regime (0<α< (4-2b)/(n)), we establish local well-posedness in L²+M^{α+2,(α+2)/(α+1)}( ⊃ L² + H^s for s>(nα)/(2(α+2))). By adapting Bourgain's high-low decomposition method, we establish global well-posedness in M^p,(p)/(p-1) with 2

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