THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS-中国期刊网

摘要 ConsidertheCauchyproblemsforann-dimensionalnonlinearsystemoffluiddynamicsequations.ThemainpurposeofthispaperistoimprovetheFouriersplittingmethodtoaccomplishthedecayestimateswithsharpratesoftheglobalweaksolutionsoftheCauchyproblems.WewillcoupletogethertheelementaryuniformenergyestimatesoftheglobalweaksolutionsandawellknownGronwall'sinequalitytoimprovetheFouriersplittingmethod.ThismethodwasinitiatedbyMariaSchonbekinthe1980'stostudytheoptimallongtimeasymptoticbehavioursoftheglobalweaksolutionsofthenonlinearsystemoffluiddynamicsequations.Asapplications,thedecayestimateswithsharpratesoftheglobalweaksolutionsoftheCauchyproblemsforn-dimensionalincompressibleNavier-Stokesequations,forthen-dimensionalmagnetohydrodynamicsequationsandformanyotherveryinterestingnonlinearevolutionequationswithdissipationscanbeestablished.

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THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

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THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

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