$L_x^2（\mathbb R^2）中具有Yukawa型势的Dirac方程的小数据散射$

IF 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations Pub Date : 2021-06-01 DOI:10.57262/die034-0708-425

Yonggeun Cho, Kiyoen Lee

{"title":"$L_x^2（\\mathbb R^2）中具有Yukawa型势的Dirac方程的小数据散射$","authors":"Yonggeun Cho, Kiyoen Lee","doi":"10.57262/die034-0708-425","DOIUrl":null,"url":null,"abstract":"We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials F [ (b + |ξ|) ] in 2 dimensions. The authors of [10, 4] obtained small data scattering and large data global well-posedness in H for s > 0, respectively. In this paper we show that the small data scattering occurs in L x (R). This can be done by combining bilinear estimates and modulation estimates of [12, 10].","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Small data scattering of Dirac equations with Yukawa type\\n potentials in $L_x^2(\\\\mathbb R^2)$\",\"authors\":\"Yonggeun Cho, Kiyoen Lee\",\"doi\":\"10.57262/die034-0708-425\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials F [ (b + |ξ|) ] in 2 dimensions. The authors of [10, 4] obtained small data scattering and large data global well-posedness in H for s > 0, respectively. In this paper we show that the small data scattering occurs in L x (R). This can be done by combining bilinear estimates and modulation estimates of [12, 10].\",\"PeriodicalId\":50581,\"journal\":{\"name\":\"Differential and Integral Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential and Integral Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/die034-0708-425\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential and Integral Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/die034-0708-425","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们重新研究了具有Yukawa型势F [(b + |ξ|)]的二维非线性质量Dirac方程的Cauchy问题。[10,4]的作者分别获得了s > 0 H下的小数据散射和大数据全局适定性。在本文中，我们证明了lx (R)中出现了小数据散射。这可以通过结合双线性估计和调制估计[12,10]来实现。

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

Small data scattering of Dirac equations with Yukawa type potentials in $L_x^2(\mathbb R^2)$

We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials F [ (b + |ξ|) ] in 2 dimensions. The authors of [10, 4] obtained small data scattering and large data global well-posedness in H for s > 0, respectively. In this paper we show that the small data scattering occurs in L x (R). This can be done by combining bilinear estimates and modulation estimates of [12, 10].

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

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.