The Cauchy problem for the fractional nonlinear Schro<spacing diaeresis>dinger equation in Sobolev spaces

被引：0

作者：

Mun, HakBom ^{[1
]}

An, JinMyong ^{[1
]}

Kim, JinMyong ^{[1
]}

机构：

[1] Kim Il Sung Univ, Fac Math, Pyongyang, North Korea

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2024年 / 31卷 / 03期

关键词：

Fractional nonlinear Schro<spacing diaeresis>dinger equation; Cauchy problem; local well-posedness; global well-posedness; Strichartz estimates; SCHRODINGER-EQUATIONS; WELL-POSEDNESS; REGULARITY;

D O I：

10.36045/j.bbms.230426

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the Cauchy problem for the fractional nonlinear Schro<spacing diaeresis>dinger (fNLS) equation. First, we establish the local well-posedness in the fractional Sobolev spaces H gamma with gamma >= 0 for the fNLS equation under less regularity assumptions for the nonlinear term than previous work. Based on the local well-posedness result, we then prove that the fNLS equation is globally wellposed in H gamma with gamma >= 0 if 4 sigma/d <= nu <= nu c(gamma) and the initial data is sufficiently small.

引用

页码：278 / 293

页数：16

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