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hyperbolic-parabolic system. We prove the global existence of a strong solution when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>H<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>L<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>-norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods.<\/jats:p>","DOI":"10.1155\/2013\/391056","type":"journal-article","created":{"date-parts":[[2013,12,15]],"date-time":"2013-12-15T21:01:21Z","timestamp":1387141281000},"page":"1-9","source":"Crossref","is-referenced-by-count":5,"title":["Global Existence and Convergence Rates for the Strong Solutions in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mrow><mml:mi>H<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>to the 3D Chemotaxis Model"],"prefix":"10.1155","volume":"2013","author":[{"given":"Weijun","family":"Xie","sequence":"first","affiliation":[{"name":"Department of Primary Education, Hunan National Vocational College, Yueyang, Hunan 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinghui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, China"},{"name":"The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuandong","family":"Xiao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995288976"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995291106"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-06-08773-9"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0252-9602(09)60059-X"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1137\/110829453"},{"issue":"1","key":"6","first-page":"27","volume":"33","year":"2012","journal-title":"Chinese Annals of Mathematics. 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