Some remarks on the inhomogeneous biharmonic NLS equation

被引：10
作者：
Guzman, Carlos M. [1 ]
Pastor, Ademir [2 ]
机构：
[1] Fluminense Fed Univ, Dept Math, Niteroi, Brazil
[2] Imecc Unicamp, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2022年 / 67卷
基金：
巴西圣保罗研究基金会;
关键词：
Inhomogeneous biharmonic nonlinear; Schrodinger equation; Global well-posedness; Critical nonlinearity; Stability theory; GLOBAL WELL-POSEDNESS; NONLINEAR SCHRODINGER-EQUATIONS; 4TH-ORDER; SCATTERING;
D O I：
10.1016/j.nonrwa.2022.103643
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the inhomogeneous biharmonic nonlinear Schrodinger equation iu(t) + Delta(2)u + lambda vertical bar x vertical bar(-b)|u|(alpha)u = 0, where lambda = +/- 1 and alpha, b > 0. In the subctritical case, we improve the global wellposedness result obtained in Guzman and Pastor (2020) for dimensions N = 5,6,7 in the Sobolev space H-2(R-N). The fundamental tools to establish our results are the standard Strichartz estimates related to the linear problem and the Hardy-Littlewood inequality. Results concerning the energy-critical case, that is, alpha = 8-2b/N-4 are also reported. More precisely, we show well-posedness and a stability result with initial data in the critical space H-2. (C) 2022 Published by Elsevier Ltd.
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页数：17
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