Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrodinger equation

被引：87

作者：

Farah, Luiz G. ^{[1
]}

机构：

[1] Univ Fed Minas Gerais, ICEx, Av Antonio Carlos,6627,Caixa Postal 702, BR-30123970 Belo Horizonte, MG, Brazil

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2016年 / 16卷 / 01期

关键词：

SCATTERING; UNIQUENESS; EXISTENCE;

D O I：

10.1007/s00028-015-0298-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the supercritical inhomogeneous nonlinear Schrodinger equation i partial derivative(t)u + Delta u + vertical bar x vertical bar(-b) vertical bar u vertical bar(2 sigma) u = 0, where and (2-b)/N < sigma < (2-b)/(N-2) and 0 < b < min{2, N}. We prove a Gagliardo-Nirenberg-type estimate and use it to establish sufficient conditions for global existence and blow-up in H-1 (R-N).

引用

页码：193 / 208

页数：16

共 50 条

[31] Local well-posedness for the inhomogeneous nonlinear Schrodinger equation in Hs(Rn)
An, JinMyong
Kim, JinMyong
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 59
[32] Global well-posedness for the Schrodinger equation coupled to a nonlinear oscillator
Komech, A. I.
Komech, A. A.
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2007, 14 (02) : 164 - 173
[33] FRACTIONAL KELLER-SEGEL EQUATION: GLOBAL WELL-POSEDNESS AND FINITE TIME BLOW-UP
Lafleche, Laurent
Salem, Samir
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2019, 17 (08) : 2055 - 2087
[34] Small Data Global Well-Posedness and Scattering for the Inhomogeneous Nonlinear Schrodinger Equation in Hs(Rn)
An, JinMyong
Kim, JinMyong
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2021, 40 (04): : 453 - 475
[35] Global well-posedness, scattering and blow-up for the generalized Boussinesq equation in high dimensions below the ground state energy
Chen, Jie
Guo, Boling
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 526 (01)
[36] On well posedness for the inhomogeneous nonlinear Schrodinger equation
Guzman, Carlos M.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2017, 37 : 249 - 286
[37] Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
Kenig, Carlos E.
Merle, Frank
ACTA MATHEMATICA, 2008, 201 (02) : 147 - 212
[38] Local well-posedness of a critical inhomogeneous Schrodinger equation
Saanouni, Tarek
Peng, Congming
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (16) : 10256 - 10273
[39] Well-posedness and blow-up phenomena for a higher order shallow water equation
Mu, Chunlai
Zhou, Shouming
Zeng, Rong
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (12) : 3488 - 3499
[40] WELL-POSEDNESS AND BLOW-UP PHENOMENA FOR A GENERALIZED CAMASSA-HOLM EQUATION
Li, Jinlu
Yin, Zhaoyang
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (10) : 5493 - 5508

← 1 2 3 4 5 →