{"title":"Scattering for Nonradial 3D NLS with Combined Nonlinearities: The Interaction Morawetz Approach","authors":"Jacopo Bellazzini, Van Duong Dinh, Luigi Forcella","doi":"10.1137/23m1559063","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3110-3143, June 2024. <br/> Abstract. We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates à la Dodson–Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1559063","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3110-3143, June 2024. Abstract. We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates à la Dodson–Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere.
Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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