Global Smooth Solution of Nonlinear Schrödinger Equation

2013/07/04 by Yongqian Han, Han, Yongqian
Engineering · Mathematics · #35Q40 #35Q55 #37K10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1307.1304

openalex publication_date 2013/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spatially periodic initial problem and Cauchy problem for nonlinear Schrödinger equations are considered. The existence and uniqueness of global solution with infinite smooth initial data u₀, i.e. u₀, |u₀|^2pu₀∈ H^∞, are established. Moreover these two problem with initial data u₀∈ H^m are globally well-posed provided the Fourier frequency of u₀ is contained in a bounded compact set. The equations studied here cover L² and H¹ critical and supercritical, defocusing and focusing nonlinear Schrodinger equations.

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