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

共 50 条

[21] NON-SYNCHRONIZED SOLUTIONS TO NONLINEAR ELLIPTIC SCHRO spacing diaeresis DINGER SYSTEMS ON A CLOSED RIEMANNIAN MANIFOLD
Mazumdar, S. A. I. K. A. T.
Vetois, J. E. R. O. M. E.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022,
[22] Existence of stable standing waves for the nonlinear Schro spacing diaeresis dinger equation with mixed power-type and Choquard-type nonlinearities
Shi, Chao
AIMS MATHEMATICS, 2022, 7 (03): : 3802 - 3825
[23] On the Cauchy problem for a nonlinear Sobolev type equation
Aristov, A. I.
DIFFERENTIAL EQUATIONS, 2014, 50 (01) : 117 - 121
[24] On the Cauchy problem for logarithmic fractional Schrödinger equation
Carles, Remi
Dong, Fangyuan
PORTUGALIAE MATHEMATICA, 2025, 82 (1-2) : 155 - 175
[25] Fractional derivatives of composite functions and the Cauchy problem for the nonlinear half wave equation
Hidano, Kunio
Wang, Chengbo
SELECTA MATHEMATICA-NEW SERIES, 2019, 25 (01):
[26] The Cauchy problem for the modified Kawahara equation in Sobolev spaces with low regularity
Yan, Wei
Li, Yongsheng
Yang, Xingyu
MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (5-6) : 1252 - 1261
[27] Global well-posedness and scattering of the four dimensional cubic focusing nonlinear Schro<spacing diaeresis>dinger system
Chang, Yonghang
Liao, Menglan
AIMS MATHEMATICS, 2024, 9 (09): : 25659 - 25688
[28] PROBABILISTIC LOCAL CAUCHY THEORY OF THE CUBIC NONLINEAR WAVE EQUATION IN NEGATIVE SOBOLEV SPACES
OH, Tadahiro
POCOVNICU, Oana
TZVETKOV, Nikolay
ANNALES DE L INSTITUT FOURIER, 2022, 72 (02) : 771 - 830
[29] ON THE GROWTH OF HIGH SOBOLEV NORMS OF THE FOURTH-ORDER SCHRO?DINGER EQUATION
Chen, Qionglei
Deng, Mingming
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2023, 36 (7-8) : 661 - 678
[30] STABILIZATION OF HIGHER ORDER SCHRO spacing diaeresis DINGER EQUATIONS ON A FINITE INTERVAL: PART II
Ozsari, Turker
Yilmaz, Kemal Cem
EVOLUTION EQUATIONS AND CONTROL THEORY, 2021, : 1087 - 1148

← 1 2 3 4 5 →