13800.帶阻尼項的歐拉方程組與液晶流方程組解的若干性質(zhì)

1、帶阻尼項的歐拉方程組與液晶流方程組解的若干性質(zhì)SomepropertiesofsolutiontotheEulerequationswithdampingandtheliquidcrystalmodel作者：董飛Author：堡i旦Q里g指導(dǎo)教師：耿金波——Supervisor：曼i墜墜殳堡旦望g一專業(yè)：基礎(chǔ)數(shù)學(xué)Major：學(xué)位：理學(xué)砸Degree：FundamentalMathematicsMasterofScience授予單位：浙江

2、師范大堂Institute：一ZhejiangNormalUniversity—May2016AbstractInthisdissertation，theresearchismainlydividedintotwoparts：OnepartisdevotedtothecomparisonofweaksolutionsoftheisentropiccompressibleEulerequationswithdampinganditspot

3、entialflowequations；TheotherpartisconcernedwiththeregularitycriterionfortheliquidcrystalsystemsinRaFollowingisthestructureofthisthesisThefirstchapteristheintroductionOnonehand，weintroducesomeinterrelatedstudiesontheisent

4、ropiccompressibleEulerequationswithdamping，andthengivesomeresearchsituationabouttheapproximateestimatesofweaksolutionsforsomeequationsinhydromechanicsanditsapproximatemodelOntheotherhand，weintroducesomeresearchbackground

5、andresearchsituationfortheliquidcrystalsystemsFinallywegiveseveralimportantdefinitionsandlemmasThesecondchapterisconcernedwiththedifferenceoftheweaksolutionsfortheisentropiccompressibleEulerequationswithdampinganditsappr

6、oximatemodelIfthesystemofisentropicflowisassumedtobeirritation，wecangetthepotentialflowequationsAstheinitialvalueofthetwoequationsismeasurablefunctionanditstotalvariationissufficientlysmall，wecanprovethatinanyboundeddoma

7、intheL1normofthedifferenceweakentropysolutionbetweensystemofisentropicflowandsystemsofpotentialflowwiththesamedatacanbeboundedbythecubeoftotalvariationsoftheinitialdataThethirdchapterisconcernedwithregularityofsolutionfo

8、rtheliquidcrystalsystemswithfractionaldiffusionsinR3TheregularityofsolutionincludetheregularityofglobalweaksolutionandtheregularityoflocalstrongsolutionInthischapterweconsidertheregularityoflocalstrongsolutionforliquidcr

9、ystalsystemsAccordingtothedifferencevalueoftherealparameterd，p，weestablishseveraldifferentregularitycriterionstoguaranteesmoothnessofsolutionsKeywords：isentropicEulerequationswithdamping；irrotationalapproximationfraction