{"title":"Remark on the Concentration Phenomenon for the Nonlinear Schrödinger Equations with a Repulsive Potential","authors":"Jun Qing, Jing Liu","doi":"10.1007/s44198-024-00166-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the blow-up solutions for the <span>\\(L^2\\)</span>-supercritical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of the new sharp Gagliardo–Nirenberg inequality proposed by Weinstein (Commun PDE 11:545–565, 1986), we obtain the <span>\\({\\dot{H}}^{s_c}\\)</span>-concentration phenomenon of blow-up solutions for this <span>\\(L^2\\)</span>-supercritical nonlinear Schrödinger equation in the space dimension <span>\\(N=2,3,4\\)</span>.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00166-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the blow-up solutions for the \(L^2\)-supercritical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of the new sharp Gagliardo–Nirenberg inequality proposed by Weinstein (Commun PDE 11:545–565, 1986), we obtain the \({\dot{H}}^{s_c}\)-concentration phenomenon of blow-up solutions for this \(L^2\)-supercritical nonlinear Schrödinger equation in the space dimension \(N=2,3,4\).
期刊介绍：
Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles.
Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics.
The main subjects are:
-Nonlinear Equations of Mathematical Physics-
Quantum Algebras and Integrability-
Discrete Integrable Systems and Discrete Geometry-
Applications of Lie Group Theory and Lie Algebras-
Non-Commutative Geometry-
Super Geometry and Super Integrable System-
Integrability and Nonintegrability, Painleve Analysis-
Inverse Scattering Method-
Geometry of Soliton Equations and Applications of Twistor Theory-
Classical and Quantum Many Body Problems-
Deformation and Geometric Quantization-
Instanton, Monopoles and Gauge Theory-
Differential Geometry and Mathematical Physics
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