三维磁流体方程的正则性研究.pdf

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1、ÆÒ10530ÆÒ200809010889©aÒO175.29?a¬ÆØ©n^6N§K5ïÄÆ<ë[9Çƶ¡êÆOÆÆÆ;Ä:êÆïÄ©§"coFn^6N§K5ïÄÆ<ë[6¶9¡9Çƶ¡êÆOÆÆÆ;Ä:êÆïÄ©§Æ?OnÆa¬ÆÇüÆØ©JFÏ"coFRegularityCriteriafortheThree-dimensionalMHDEquationsCandidateYongyeZhaoSupervisorProfessor.Yuelong-Xiao

2、CollegeMathematicsandComputationalScienceProgramPureMathematicsSpecializationPartialDifferentialEquationDegreeMasterofScienceUniversityXiangtanUniversityDateApril20th,2011ÆÆØ©M5(²¤J¬"é©ïÄÑz

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7、;f);r);K5IAbstractUsually§wehopethesolutionsofthePartialDifferentialEquationstobesmoothenoughtoqualifyasaclassicalsol

8、ution.Thisleadstothestudyofregu-larityofweaksolutions.Asweallknow,theexistenceofweaksolutionsdependsonsimpleestimatesplusideaoffunctionalanalysis,whereastheregularityoftheweaksolutions,whentrue,usuallyrestsuponmanyintricatecalculusestimates.Inthispaper,byusingsome

9、classicalinequalities,weconsiderregularitycriteriaforsolutionstothe3DMHDequationswithincompressibleconditionsandobtainanewresult.Thisarticleisdividedinto4chapters.Chapter1isintroduction.Chapter2isthepreliminariesneededintheproofsoftheconclusions.InChapter3,weprove

10、theregularitycriterionforsolutionsofthree-dimensionalMHDequationswithincompressibleconditions.Finally,weconcludeinChapter4andgivesomecommentsonpossiblefuturework.KeyWords:MHDEquations;Weaksolution;Strongsolution;Regu-larityII8¹1ÙÚó.................................

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