LOCAL WELL-POSEDNESS OF THE FRACTIONAL INHOMOGENEOUS NLS IN SOBOLEV SPACES

被引：0

作者：

Ghanmi, Radhia ^{[1
]}

Boulaaras, Salah ^{[2
]}

Saanouni, Tarek ^{[2
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, LR03ES04 partial differential equat & applicat, Tunis 2092, Tunisia

[2] Qassim Univ, Dept Math, Coll Sci, Buraydah 51452, Saudi Arabia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年

关键词：

Inhomogeneous fractional Schro<spacing diaeresis>dinger problem; nonlinear equations; local theory;

D O I：

10.3934/dcdss.2024069

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work proves the local existence of solutions to some inhomogeneous nonlinear equations of Schro<spacing diaeresis>dinger type with a fractional Laplacian in Sobolev spaces. Moreover, for small datum, the local solution extends to a global one. We give an elementary proof based on Strichartz estimates coupled with a fix point argument. In order to avoid a loss of regularity in Strichartz estimates, we consider radial data.

引用

页数：11

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