Global well-posedness for the higher order non-linear Schrödinger equation in modulation spaces

被引：0
|
作者：
Carvajal, X. [1 ]
Gamboa, P. [1 ]
Santos, R. [2 ]
机构：
[1] Univ Fed Rio de Janeiro UFRJ, Inst Matemat, BR-21941909 Rio De Janeiro, RJ, Brazil
[2] Univ Fed Rio de Janeiro UFRJ, Inst Politecn, BR-2793056 Macae, RJ, Brazil
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 543卷 / 02期
关键词：
Schrodinger equation; Korteweg-de Vries ewuation; Initial value problem; Well-posedness; Sobolev spaces; Modulation spaces; INTEGRABLE GROUP-REPRESENTATIONS; MODIFIED KDV EQUATION;
D O I：
10.1016/j.jmaa.2024.128985
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the initial value problem (IVP) associated with a higher order non-linear Schr & ouml;dinger (h-NLS) equation partial derivative tu+ia partial derivative x2u+b partial derivative x3u=2ia|u|2u+6b|u|2 partial derivative xu,x,t is an element of R,with given data in the modulation space Ms2,p(R). Using ideas from Killip, Visan, Zhang, Oh and Wang, we prove that the IVP associated with the h-NLS equation is globally well-posed in the modulation spaces Ms2,p(R) for s >= 14 and p >= 2. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining. AI training and similar technologies
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