Sharp well-posedness and ill-posedness results for the inhomogeneous NLS equation

被引：0

作者：

Campos, Luccas ^{[1
]}

Correia, Simao ^{[2
]}

Farah, Luiz Gustavo ^{[1
]}

机构：

[1] Univ Fed Minas Gerais, Dept Math, Ave Pres Antonio Carlos, 6627, Pampulha, BR-31270901 Belo Horizonte, MG, Brazil

[2] Univ Lisbon, Ctr Math Anal Geometry & Dynam Syst, Inst Super Tecn, Dept Math, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2025年 / 85卷

基金：

巴西圣保罗研究基金会;

关键词：

Inhomogeneous Schr & ouml; dinger equation; Local well-posedness; Fractional Leibniz rule; Ill-posedness; NONLINEAR SCHRODINGER-EQUATION;

D O I：

10.1016/j.nonrwa.2025.104336

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial value problem associated to the inhomogeneous nonlinear Schrodinger equation, iu(t )+ Delta u + mu|x|(-b)|u|(alpha)u = 0, u(0 )is an element of H-s(R-N) or u(0 )is an element of H-s(R-N), with mu = +/- 1, b > 0, s >= 0 and 0 < alpha <= 4-2b/N-2s (0 < alpha < infinity if s >= N/2). By means of an adapted version of the fractional Leibniz rule, we prove new local well-posedness results in Sobolev spaces for a large range of parameters. We also prove an ill-posedness result for this equation, through a delicate analysis of the associated Duhamel operator.

引用

页数：21

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