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
收藏
页码：278 / 293
页数：16
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