径向能量临界半线性热方程的局部序贯鼓泡

IF 0.8 Q2 MATHEMATICS

Vietnam Journal of Mathematics Pub Date : 2023-09-26 DOI:10.1007/s10013-023-00648-w

Andrew Lawrie

{"title":"径向能量临界半线性热方程的局部序贯鼓泡","authors":"Andrew Lawrie","doi":"10.1007/s10013-023-00648-w","DOIUrl":null,"url":null,"abstract":"Abstract In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded $$\\dot{H} ^1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msup> </mml:math> norm. The proof uses a combination of Gérard’s profile decomposition (ESAIM Control Optim. Calc. Var. 3 : 213–233, 1998), concentration compactness techniques in the spirit of Duyckaerts, Kenig, and Merle’s seminal work (Geom. Funct. Anal. 22 : 639–698, 2012), and a virial argument in the spirit of Jia and Kenig’s work (Amer. J. Math. 139 : 1521–1603, 2017) to deduce the vanishing of the error in the neck regions between the bubbles. The argument is based closely on an analogous lemma proved in the author’s recent work with Jendrej (arXiv:2210.14963, 2022) on the equivariant harmonic map heat flow in dimension two.","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation\",\"authors\":\"Andrew Lawrie\",\"doi\":\"10.1007/s10013-023-00648-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded $$\\\\dot{H} ^1$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:msup> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msup> </mml:math> norm. The proof uses a combination of Gérard’s profile decomposition (ESAIM Control Optim. Calc. Var. 3 : 213–233, 1998), concentration compactness techniques in the spirit of Duyckaerts, Kenig, and Merle’s seminal work (Geom. Funct. Anal. 22 : 639–698, 2012), and a virial argument in the spirit of Jia and Kenig’s work (Amer. J. Math. 139 : 1521–1603, 2017) to deduce the vanishing of the error in the neck regions between the bubbles. The argument is based closely on an analogous lemma proved in the author’s recent work with Jendrej (arXiv:2210.14963, 2022) on the equivariant harmonic map heat flow in dimension two.\",\"PeriodicalId\":45919,\"journal\":{\"name\":\"Vietnam Journal of Mathematics\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vietnam Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s10013-023-00648-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vietnam Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10013-023-00648-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文证明了具有有界$$\dot{H} ^1$$ H˙1范数的能量临界非线性热方程解的一个局域冒泡结果。该证明使用了gsamim的配置文件分解(ESAIM Control Optim)的组合。Calc. Var. 3: 213 - 233,1998)，在Duyckaerts, Kenig和Merle的开创性工作的精神集中密实技术(Geom。函数。《论文集》，2012年第22期:639-698页)，以及在贾和柯尼格的作品精神中进行的一场病毒式辩论(美国)。[j] .数学学报，39(1):1521-1603,2017)，以推断气泡之间的颈部区域误差的消失。该论证紧密地基于作者最近与Jendrej (arXiv:2210.14963, 2022)在二维等变调和映射热流上证明的一个类似引理。

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

Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation

Abstract In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded $$\dot{H} ^1$$ H ˙ 1 norm. The proof uses a combination of Gérard’s profile decomposition (ESAIM Control Optim. Calc. Var. 3 : 213–233, 1998), concentration compactness techniques in the spirit of Duyckaerts, Kenig, and Merle’s seminal work (Geom. Funct. Anal. 22 : 639–698, 2012), and a virial argument in the spirit of Jia and Kenig’s work (Amer. J. Math. 139 : 1521–1603, 2017) to deduce the vanishing of the error in the neck regions between the bubbles. The argument is based closely on an analogous lemma proved in the author’s recent work with Jendrej (arXiv:2210.14963, 2022) on the equivariant harmonic map heat flow in dimension two.

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

Vietnam Journal of Mathematics MATHEMATICS-

CiteScore

1.90

自引率

0.00%

发文量

期刊介绍： Vietnam Journal of Mathematics was originally founded in 1973 by the Vietnam Academy of Science and Technology and the Vietnam Mathematical Society. Published by Springer from 1997 to 2005 and since 2013, this quarterly journal is open to contributions from researchers from all over the world, where all submitted articles are peer-reviewed by experts worldwide. It aims to publish high-quality original research papers and review articles in all active areas of pure and applied mathematics.