一类导数为非线性的Schrödinger非线性方程的若干结果

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2026-04-02 DOI:10.1111/sapm.70211

Liuyan Huang, Guoqing Zhang

{"title":"一类导数为非线性的Schrödinger非线性方程的若干结果","authors":"Liuyan Huang, Guoqing Zhang","doi":"10.1111/sapm.70211","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, we consider a class of nonlinear Schrödinger equations with derivative nonlinearities, which is first introduced by Colin and Colin [<i>Differential Integral Equations</i> 17 (2004): 297–330] as a model of laser-plasma interaction. Based on concentration-compactness principle combined with variational methods, we prove some existence and nonexistence results of normalized ground states, respectively. Furthermore, we obtain the global well-posedness in three-dimensional space. By using conservation laws and Virial estimate, we also investigate some blow-up results.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"156 4","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2026-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Results for a Class of Nonlinear Schrödinger Equations With Derivative Nonlinearities\",\"authors\":\"Liuyan Huang, Guoqing Zhang\",\"doi\":\"10.1111/sapm.70211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In this paper, we consider a class of nonlinear Schrödinger equations with derivative nonlinearities, which is first introduced by Colin and Colin [<i>Differential Integral Equations</i> 17 (2004): 297–330] as a model of laser-plasma interaction. Based on concentration-compactness principle combined with variational methods, we prove some existence and nonexistence results of normalized ground states, respectively. Furthermore, we obtain the global well-posedness in three-dimensional space. By using conservation laws and Virial estimate, we also investigate some blow-up results.</p></div>\",\"PeriodicalId\":51174,\"journal\":{\"name\":\"Studies in Applied Mathematics\",\"volume\":\"156 4\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2026-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studies in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70211\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.70211","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑由Colin和Colin[微分积分方程17(2004):297-330]首先引入的一类具有导数非线性的非线性Schrödinger方程作为激光-等离子体相互作用的模型。基于浓度-紧致原理，结合变分方法，分别证明了归一化基态的存在性和不存在性。进一步，我们得到了三维空间的全局适定性。利用守恒定律和维里估计，我们还研究了一些爆破结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Some Results for a Class of Nonlinear Schrödinger Equations With Derivative Nonlinearities

In this paper, we consider a class of nonlinear Schrödinger equations with derivative nonlinearities, which is first introduced by Colin and Colin [Differential Integral Equations 17 (2004): 297–330] as a model of laser-plasma interaction. Based on concentration-compactness principle combined with variational methods, we prove some existence and nonexistence results of normalized ground states, respectively. Furthermore, we obtain the global well-posedness in three-dimensional space. By using conservation laws and Virial estimate, we also investigate some blow-up results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.