资源描述：
《3维非齐次不可压Navier-Stokes方程组在旋度边界条件下的消失粘性极限问题.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、˖ڍመڙጲhttp://www.paper.edu.cn3维非齐次不可压Navier-Stokes方程组在旋度边界条件下的消失粘性极限问题陈鹏飞，肖跃龙湘潭大学数学与计算科学学院学院，湘潭市 邮编411105摘要：本文主要研究在一般光滑有界区域R3的情形时，考虑了3维非齐次不可压Navier-Stoke方程组在一类旋度边界条件下的消失粘性极限问题。在文章中建立了这类初边值问题强解的局部存在性，然后证明了消失粘性极限的过程，得到了强解的一个收敛率的结果。关键词：非齐次不可压Navier-Stokes方程；旋度边界条件；消失粘性极限中图分类号
2、：35Q30;76D05OntheVanishingViscosityLimitforthe3DNonhomogeneousIncompressibleNavier-StokesEquationwithavorticityBoundaryConditionCHENPeng-Fei,XIAOYue-LongDepartmentofMathematicsandComputationalScienceUniversityofXiangtan,Xiangtan411105Abstract:Thispaperconcernsthethree-dimens
3、ionalnonhomogeneousincompressibleNavier-StokesequationwithaclassofvorticityboundaryconditiononsmoothboundeddomaininR3.Itestablishesthelocalwell-posednessofthestrongsolutionforinitialboundaryvalueproblemforsuchsystems.Furthermore,thevanishingviscositylimitofthenonhomogeneousi
4、ncompressibleNavier-Stokessystemisprovedandarateofconvergenceestimatesisshownforthestrongsolution.Keywords:NonhomogeneousincompressibleNavier-Stokesequation,Avorticityboundaryconditions,Vanishingviscositylimit.Foundations:ThisworkwassupportedbyResearchFundfortheDoctoralProgr
5、amofHigherEducationofChi-na(20134301110008)andtheHunanProvincialInnovationFoundationForPostgraduate(CX2015B205)AuthorIntroduction:Correspondenceauthor：XIAOYue-Long（1961-），male，professor，majorresearchdirection：Partialdifferentialequation.CHENPeng-Fei（1987-），male，doctor，majorre
6、searchdirection：Partialdifferentialequation.Email：cpfxtu@163.com-1-˖ڍመڙጲhttp://www.paper.edu.cn0IntroductionLetΩ⊂R3beaboundedsmoothdomain,theinitialboundaryvalueproblemofthenonhomogeneousincompressibleNavier-Stokesequationisgivenbyρ∂tu−ν∆u+ρu·∇u+∇p=0,inΩ,(1)∂tρ+u·∇ρ=0,inΩ,
7、(2)∇·u=0,inΩ,(3)u(0,x)=u0,ρ(0,x)=ρ0,inΩ,(4)equippedwiththefollowingvorticityboundaryconditionsu·n=0,ω·n=0,n×(∆u)=0on∂Ω.(5)Heretheconstantν>0,n,ρ,u,prepresenttheviscositycoefficient,theoutwardunitnormalvector,themassdensity,thevelocityfieldandthepressureofthefluids,respectively.T
8、heinitialdensityρ0(x)isassumedtosatisfytheconditionm≤ρ0(x)≤MwithmandMbounde
