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 / 17卷 / 10期

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

页码：3035 / 3045

页数：11

共 50 条

[41] On Well-Posedness of the Cauchy Problem for Pseudohyperbolic Equations in Weighted Sobolev Spaces
L. N. Bondar
G. V. Demidenko
Siberian Mathematical Journal, 2023, 64 : 1076 - 1090
[42] Well-Posedness for the Navier-Stokes Equations with Datum in the Sobolev Spaces
Khai D.Q.
Acta Mathematica Vietnamica, 2017, 42 (3) : 431 - 443
[43] Energy conservation and well-posedness of the Camassa–Holm equation in Sobolev spaces
Yingying Guo
Weikui Ye
Zeitschrift für angewandte Mathematik und Physik, 2023, 74
[44] Well-posedness in weighted Sobolev spaces for elliptic equations of Cordes type
Loredana Caso
Roberta D’Ambrosio
Maria Transirico
Collectanea Mathematica, 2016, 67 : 539 - 554
[45] On Well-Posedness and Concentration of Blow-Up Solutions for the Intercritical Inhomogeneous NLS Equation
Cardoso, Mykael
Farah, Luiz Gustavo
Guzman, Carlos M.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2023, 35 (02) : 1337 - 1367
[46] Well-posedness of the Cauchy problem of Ostrovsky equation in anisotropic Sobolev spaces
Wang, Hua
Cui, Shangbin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (01) : 88 - 100
[47] Well-posedness of the Muskat problem in subcritical Lp-Sobolev spaces
Abels, H.
Matioc, B-, V
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2022, 33 (02) : 224 - 266
[48] Well-posedness of the Cauchy problem for the Hirota equation in Sobolev spaces Hs
Huo, ZH
Guo, BL
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (06) : 1093 - 1110
[49] Unconditional well-posedness for subcritical NLS in HS
Rogers, Keith M.
COMPTES RENDUS MATHEMATIQUE, 2007, 345 (07) : 395 - 398
[50] On Well-Posedness and Concentration of Blow-Up Solutions for the Intercritical Inhomogeneous NLS Equation
Mykael Cardoso
Luiz Gustavo Farah
Carlos M. Guzmán
Journal of Dynamics and Differential Equations, 2023, 35 : 1337 - 1367

← 1 2 3 4 5 →