GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION
For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dicho...
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| Veröffentlicht in: | Acta mathematica scientia 2017-07, Vol.37 (4), p.941-948 |
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| creator | 杨凌燕 李晓光 吴永洪 Louis CA CCETTA |
| description | For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）. |
| doi_str_mv | 10.1016/S0252-9602(17)30049-8 |
| format | Article |
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Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.</description><identifier>ISSN: 0252-9602</identifier><identifier>EISSN: 1572-9087</identifier><identifier>DOI: 10.1016/S0252-9602(17)30049-8</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>35J10 ; 35Q55 ; blow-up solution ; Hartree equation ; Threshold criteria ; 二分法 ; 基态 ; 整体存在 ; 整体适定性 ; 方程 ; 柯西问题 ; 爆破</subject><ispartof>Acta mathematica scientia, 2017-07, Vol.37 (4), p.941-948</ispartof><rights>2017 Wuhan Institute of Physics and Mathematics</rights><rights>Copyright © Wanfang Data Co. Ltd. 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Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.</description><subject>35J10</subject><subject>35Q55</subject><subject>blow-up solution</subject><subject>Hartree equation</subject><subject>Threshold criteria</subject><subject>二分法</subject><subject>基态</subject><subject>整体存在</subject><subject>整体适定性</subject><subject>方程</subject><subject>柯西问题</subject><subject>爆破</subject><issn>0252-9602</issn><issn>1572-9087</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNqFUEtPwjAcb4wmIvoRTBZPcpj2sa6rFzOgPJKFIRvh2JTS4QhuuqHgt7c89Orpn_zzewNwi-ADgsh_TCCm2OU-xPeItQiEHneDM9BAlNk3DNg5aPxBLsFVXa-g5WHfa4CnfhS3w8iZiShyx3EiuiORJE446jrtKJ6507HTiydOOhDOIJykEyEc8TIN02E8ugYXmVrX5uZ0m2DaE2ln4EZxf9gJI1cTBjeu72mCKefUKJzBgMwhxZ5mRDPEMk8xnPlmTqCvAkMQXSjNDc-U9hZUm4WHKWmC1lF3q4pMFUu5Kj-rwjrKerdd7-bSYIgY9Gxvi6VHrK7Kuq5MJt-r_E1V3xJBuR9LHsaS-yUkYvIwlgws7_nIM7bIV24qWevcFDZBXhm9kYsy_1fh7uT8WhbLj9zm_LX2GQ44JTwgP_23df0</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>杨凌燕 李晓光 吴永洪 Louis CA CCETTA</creator><general>Elsevier Ltd</general><general>Sichuan Normal University,Chengdu,610066,China%Sichuan Normal University,Chengdu,610066,China</general><general>Wuhan Institute of Physics and Machematics Chinese Academy of Science,Wuhan 430071,China%Department of Mathematics and Statistics,Curtin University of Technology,Perth,WA 6845,Australia</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20170701</creationdate><title>GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION</title><author>杨凌燕 李晓光 吴永洪 Louis CA CCETTA</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-64c325995ea2f083b0524c73c717f4a72f6eb306a8e315dac9e9fac4d5ced4253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>35J10</topic><topic>35Q55</topic><topic>blow-up solution</topic><topic>Hartree equation</topic><topic>Threshold criteria</topic><topic>二分法</topic><topic>基态</topic><topic>整体存在</topic><topic>整体适定性</topic><topic>方程</topic><topic>柯西问题</topic><topic>爆破</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>杨凌燕 李晓光 吴永洪 Louis CA CCETTA</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Acta mathematica scientia</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>杨凌燕 李晓光 吴永洪 Louis CA CCETTA</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION</atitle><jtitle>Acta mathematica scientia</jtitle><addtitle>Acta Mathematica Scientia</addtitle><date>2017-07-01</date><risdate>2017</risdate><volume>37</volume><issue>4</issue><spage>941</spage><epage>948</epage><pages>941-948</pages><issn>0252-9602</issn><eissn>1572-9087</eissn><abstract>For 2 〈 y 〈 min{4, n}, we consider the focusing Hartree equation iut ＋ Au ＋ （｜x｜^-γ ＊ ｜u｜2）u = O, x∈ R^n Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of - △ ＋ Q = （｜x｜^-γ ＊ ｜Q｜^2）Q. Guo and Wang [Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of （0,1） if M[u]^l-ScE[u]^Sc 〈 M[Q] ^1-sc E[Q] ^（sc= r-2/2）. In this paper, we consider the complementary case M[u]^1-ScE[u]^sc 〉_ M[Q]^1-sc and obtain a criteria on blow-up and global existence for the Hartree equation （0.1）.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/S0252-9602(17)30049-8</doi><tpages>8</tpages></addata></record> |
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| subjects | 35J10 35Q55 blow-up solution Hartree equation Threshold criteria 二分法 基态 整体存在 整体适定性 方程 柯西问题 爆破 |
| title | GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION |
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