不可压boussinesq方程的全局正则性

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1、Æ“Ò10530ÆÒ201510111122©aÒO175.24—?úma¬ÆØ©ØŒØBoussinesq•§ÛK5Æž<šSs•“"Œ©Çƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••‡©•§"˜lco›FØŒØBoussinesq•§ÛK5Æž<šSs“6¶9…¡"Œ©Çƶ¡êƆOŽ‰ÆÆƉ;’êÆïÄ••‡©•§Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ"˜lco›FGlobalregularityofincompressibleBoussinesqequationsCandidateKongChunliSupe

2、rvisorProfessorTangTai-ManCollegeMathematicsandComputationalScienceProgramMathematicsSpecializationPartialDierentialEquationDegreeMasterofScienceUniversityXiangtanUniversityDateApril10,2018Á‡©?ØÃ9DØŒØBoussinesq•§ÛK5¯K§^aquChae?Ø3‘ØŒØî.•§•{§Ñ2†3‘ÃÊ5Ã9DBoussi-nesq•§ÛÜ1w)÷Ÿ:;,»¿©^

3、‡.q^Chae?n3‘ØŒØEuler9Navier-Stokes•§•{§é2Ú3‘Ã9DBoussinesq•§§^aquµÝ[U£enstrophy¤þ,‰Ñ»^‡.32‘,Ê5XêŒu0ž§®•T•§´ÛK.'…c:Boussinesq•§;ÛK5;»^‡;Ÿ:;,.IAbstractInthispaper,wediscusstheglobalregularityoftheincompressibleBoussinesqequationswithoutheatconduction.UsingamethodChaeusedtodiscusst

4、hethreedimensionalincompressibleEulerequations,weobtainasucientconditionforthelocalsmoothsolutionofthetwoorthreedimensionalinviscidBoussinesqequationswithoutheatconductiontoblowupalongparticletrajectories.UsingamethodthatChaeusedindiscussingthethreedimensionalincompressibleEulerandNavie

5、r-Stokesequations,weusequantitiessimilartotheenstrophytogiveabolw-upconditionforlocalsmoothsolutionsofthetwoandthreedimensionalBoussinesqequationswithoutheatconduction.Inthetwodimensioncase,theequationsisknowntobegloballyregularwhentheviscosityisgreaterthanzero.KeyWords:Boussinesqequatio

6、ns;globallyregularity;blow-upcriterion;parti-cletrajectories.II8¹1˜ÙÚó.......................................................11.1ïįK.....................................................11.2ïĵ.......................................................11.3©óŠ.............................

7、........................31Ùý•£.................................................61nÙÃÊ5Ã9DBoussinesq•§ÛÜ1w)÷Ÿ:;,»^‡y²........................................................91oÙÃ9DBoussinesq•§

8、ÛÜ1w)ŠâaquµÝ[U£enstrophy¤þ‰Ñ»^‡y²............................151ÊÙo(†Ð".