带γ-law相对论欧拉方程组熵解非相对论整体极限

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1、上海交通大学硕士学位论文带γ-law的相对论欧拉方程组熵解的非相对论整体极限姓名：任绪才申请学位级别：硕士专业：基础数学指导教师：李亚纯20060101þ°ÏÆÆØ©M5(²L¬¤J"é©ïÄÑz<Ú8N§þ®3©±²(ªI²"<¿£(²{Æ(Jd<«ú"ÆØ©ö¶:FÏ:cFþ°ÏÆÆØ©¦^ÇÖÆØ©ö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿I[k'ܽÅxØ©E<Ú>f§#NØ©Ú/

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14、1Non-RelativisticGlobalLimitsofEntropySolutionstotheRelativisticEulerEquationswithγ−lawABSTRACTWestudytheglobalentropysolutionsoftherelativisticEulerequationswhichrepresenttheconservationofenergyandmomentumwithanequationofsatep=κ2ργ(γ>1).WeshowthattheentropysolutionsoftherelativisticEuler

15、equationsconvergetotheentropysolutionsofthenon-relativisticEulerequationsasc(thelightspeed)→+∞.Astoexistencefortheequationsunderconsideration,someresults:J.SmollerandB.Temple[23]forγ=1case,J.Chen[6]forγ>1case,andY.C.Li,D.M.FengandZ.J.Wang[13]foraclassoflargeinitialdata,etc.Inthecaseofp=σ2ρ,theglo

16、balweaksolutionsoftherelativisticEulersystemconvergetothesolutionsofthenon-relativisticEulerequationsystem,asc→+∞,whichhasbeenprovedbyLuMinandSeijiUkai[17].OurresultsarebasedontheGlimmSchemeandmeticulousestimatesoftheglobalbehaviorofthenon-linearwaves.Westartfromanintroductiontothegeneralconserva

17、tionlaws.AfterdeducingtherelativisticEulerequationsphysically,wepresentmoredetailedmathematicalpropertiesofthissystem.ByestimatingtheapproximatesolutionsconstructedbyGlimmdifferencescheme,wefindthatthecoefficientsareindepe