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1、LectureNotesinMathematics1971Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisLaureSaint-RaymondHydrodynamicLimitsoftheBoltzmannEquation123LaureSaint-RaymondDépartementdeMathématiquesetApplicationsEcoleNormaleSupérieure45ruedUlm75005ParisFrancelaure.saint-raymond@ens.frISBN:978-3-540-
2、92846-1e-ISBN:978-3-540-92847-8DOI:10.1007/978-3-540-92847-8LectureNotesinMathematicsISSNprintedition:0075-8434ISSNelectronicedition:1617-9692LibraryofCongressControlNumber:2008943981MathematicsSubjectClassification(2000):76-02,76P05,82C40,35B40,35A99c2009Springer-VerlagBerlinHeidelbergThiswork
3、issubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonly
4、undertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabs
5、enceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:SPiPublisherServicesPrintedonacid-freepaperspringer.comPrefaceThematerialpublishedinthisvolumecomesessentiallyfromacoursegivenattheConferenceonBoltzmannequationand
6、
uidodynamiclimits",heldinTriesteinJune2006.TheauthorisverygratefultoFabioAnconaandStefanoBianchinifortheirinvitation,andtheirencouragementstowritetheselecturenotes.Theaimofthisbookistopresentsomemathematicalresultsdescribingthetransitionfromkinetictheory,andmorepreciselyfromtheBoltzmannequatio
7、nforperfectgasestohydrodynamics.Di erent
uidasymptoticswillbeinvestigated,startingalwaysfromsolutionsoftheBoltzmannequationwhichareonlyassumedtosatisfytheestimatescomingfromphysics,namelysomeboundsonmass,energyandentropy.Inparticu
