{"title":"n = 4维半波图的小数据全局正则性。","authors":"Anna Kiesenhofer, Joachim Krieger","doi":"10.1080/03605302.2021.1936021","DOIUrl":null,"url":null,"abstract":"<p><p>We prove that the half-wave maps problem on <math> <mrow> <msup><mrow><mi>R</mi></mrow> <mrow><mn>4</mn> <mo>+</mo> <mn>1</mn></mrow> </msup> </mrow> </math> with target <i>S</i> <sup>2</sup> is globally well-posed for smooth initial data which are small in the critical <i>l</i> <sup>1</sup> based Besov space. This is a formal analogue of the result proved by Tataru for wave maps.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/03605302.2021.1936021","citationCount":"5","resultStr":"{\"title\":\"Small data global regularity for half-wave maps in <i>n</i> = 4 dimensions.\",\"authors\":\"Anna Kiesenhofer, Joachim Krieger\",\"doi\":\"10.1080/03605302.2021.1936021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We prove that the half-wave maps problem on <math> <mrow> <msup><mrow><mi>R</mi></mrow> <mrow><mn>4</mn> <mo>+</mo> <mn>1</mn></mrow> </msup> </mrow> </math> with target <i>S</i> <sup>2</sup> is globally well-posed for smooth initial data which are small in the critical <i>l</i> <sup>1</sup> based Besov space. This is a formal analogue of the result proved by Tataru for wave maps.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2021-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/03605302.2021.1936021\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/03605302.2021.1936021\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2021/1/1 0:00:00\",\"PubModel\":\"eCollection\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2021.1936021","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2021/1/1 0:00:00","PubModel":"eCollection","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Small data global regularity for half-wave maps in n = 4 dimensions.
We prove that the half-wave maps problem on with target S2 is globally well-posed for smooth initial data which are small in the critical l1 based Besov space. This is a formal analogue of the result proved by Tataru for wave maps.
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