三维不均匀不可压Navier-Stokes方程经典解的爆破准则.pdf

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1、Æ“Ò10530ÆÒ201009011048©aÒO175.29—?a¬ÆØ©n‘Øþ!ØŒØNavier-Stokes•§²;)»OKÆž<A•“"Œ©Çƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••‡©•§"˜nco›Fn‘Øþ!ØŒØNavier-Stokes•§²;)»OKÆž<A“6¶9…¡"Œ©Çƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••‡©•§Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ"˜nco›FAblow-upcriterionforclassicalso

2、lutionstothe3-DinhomogeneousincompressibleNavier-StokesequationsCandidateNaWangSupervisorProfessor.TANGTai-ManCollegeMathematicsandComputationalScienceProgramPureMathematicsSpecializationPartialDierentialEquationDegreeMasterofScienceUniversityXiangtanUniversityD

3、ateApril10th,2013‰ŒÆÆØ©M5(²¤JŠ¬"é©ïĉѕ‡z‡<Ú8N§þ®3©¥±²(•ªI²"<¿£(²{ÆJd<«ú"Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡§#NØ©Ú/"<ljŒÆŒ±òÆ

4、Ø©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K3)‰Ñ˜‡r)»^‡.éu

5、©ïÄ•§§Kim(2006)±„ÝLs(Lr).‰ê(2+3=1;3

6、thevelocityforclassicalsolutionstothethreedimensionalinhomogeneousincompressibleNavier-Stokesequations.Itmaybehelpfulininvestigatingtheglobalexistenceofclassicalsolutions,theuniquenessofweaksolutionsandthemannerinwhichclassicalsolutionsblowupiftheydo.Forthedensit

7、y-dependentNavier-Stokesequations,ChoandKim(2004)havederivedablow-upcriterionforstrongsolutionsintermsoftheL1(L2)-normofthegradientofthevelocityandtheL1(Lq)-normofthegradientofthedensityforanyq>3.Fortheequationsinthispaper,Kim(2006)hasderivedablow-upcriterionfors

8、trongsolutionsintermsoftheLs(Lr)-normofthevelocityforany(r;s)with2+3=1and3