Local existence of strong solutions to the generalized Boussinesq equations

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1、ApplicableAnalysisAnInternationalJournalISSN:0003-6811(Print)1563-504X(Online)Journalhomepage:http://www.tandfonline.com/loi/gapa20LocalexistenceofstrongsolutionstothegeneralizedBoussinesqequationsZaihongJiang,BaixinLiu&CaochuanMaTocitethisarticle:ZaihongJiang,BaixinLiu&Caochu

2、anMa(2016):LocalexistenceofstrongsolutionstothegeneralizedBoussinesqequations,ApplicableAnalysis,DOI:10.1080/00036811.2016.1155209Tolinktothisarticle:http://dx.doi.org/10.1080/00036811.2016.1155209Publishedonline:08Mar2016.SubmityourarticletothisjournalViewrelatedarticlesViewC

3、rossmarkdataFullTerms&Conditionsofaccessandusecanbefoundathttp://www.tandfonline.com/action/journalInformation?journalCode=gapa20Downloadby:[NewYorkUniversity]Date:10March2016,At:04:39APPLICABLEANALYSIS,2016http://dx.doi.org/10.1080/00036811.2016.1155209Localexistenceofstrongs

4、olutionstothegeneralizedBoussinesqequationsZaihongJianga,BaixinLiuaandCaochuanMaa,baDepartmentofMathematics,ZhejiangNormalUniversity,Jinhua,China;bDepartmentofMathematics,TianshuiNormalUniversity,Tianhui,ChinaABSTRACTARTICLEHISTORYThispaperdealswiththelocalexistenceanduniquene

5、ssofstrongsolutionsReceived29September2015forthegeneralizedBoussinesqequationswithfractionaldissipation.AsaAccepted11February2016corollary,weestablishsomeregularitycriteriatoguaranteesmoothnessofCOMMUNICATEDBYsolutions.B.AmazianeKEYWORDSGeneralizedBoussinesqequations;localexis

6、tenceAMSSUBJECTCLASSIFICATIONS35B65;35A01;35A021.IntroductionWeconsiderthefollowinggeneralizedBoussinesqequations:u2αn+t+u·∇u+∇p+νu=θen,(x,t)∈R×R,(1.1)θ2βθ=0,(x,t)∈Rn×R+,(1.2)t+u·∇θ+κdivu=0,(x,t)∈Rn×R+,(1.3)(u,θ)(x,0)=(un0,θ0),x∈R,(1.4)wheren=2,3,u=u(x,t),θ=θ(x,t)andp=p(x,t)

7、representtheunknownvelocityfield,theDownloadedby[NewYorkUniversity]at04:3910March2016temperature,andthepressureoftheflow,respectively.Theparametersα≥0,β≥0arerealanden=(0,0,···,1)denotestheunitvectorintheverticaldirection.Theconstantsν≥0andκ≥0are1calledviscosityandthermaldiffusivi

8、ty,respectively.Inaddition,=(−)2denotestheZygmundoperator,w