Hydrodynamic Limits of the Boltzmann Equation

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1、dafermos2v.2005/04/29Prn:8/06/2005;8:46F:dafermos203.tex;VTEX/Linap.111223CHAPTER33445566TheBoltzmannEquationand778ItsHydrodynamicLimits899101011111212FrançoisGolse131314InstitutUniversitairedeFrance,andLaboratoireJacques-LouisLions,UniversitéParis7,14BoîteCourr

2、ier187,F75252ParisCedex05,France1515E-mail:golse@math.jussieu.fr16161717181819Contents191.Introduction..................................................320202.Fluiddynamics:Apresentationofmodels..................................521212.1.ThecompressibleEulersyste

3、m....................................7222.2.ThecompressibleNavierStokessystem...............................922232.3.Theacousticsystem..........................................1023242.4.TheincompressibleEulerequations..................................1124252.5.T

4、heincompressibleNavierStokesequations............................13252.6.Thetemperatureequationforincompressibleflows.........................1426262.7.Couplingofthevelocityandtemperaturefieldsbyconservativeforces..............1427273.TheBoltzmannequationanditsfor

5、malproperties.............................16283.1.Conservationlaws...........................................1928293.2.BoltzmannsH-theorem........................................2329303.3.H-theoremandaprioriestimates...................................26303.4.Fur

6、therremarksontheH-theorem..................................3431313.5.Thecollisionkernel..........................................3732323.6.Thelinearizedcollisionintegral....................................44334.HydrodynamicscalingsfortheBoltzmannequation........

7、....................5133344.1.Notionofararefiedgas........................................5134354.2.ThedimensionlessBoltzmannequation................................5335365.CompressiblelimitsoftheBoltzmannequation:Formalresults......................55365.1.Thecom

8、pressibleEulerlimit:TheHilbertexpansion........................5537375.2.ThecompressibleNavierStokeslimit:TheChapmanEnskogexpansion.............5938385.3.Thecompressi