Diffuse interface models for two phase flows of viscous imcompressible fluids.pdf

《Diffuse interface models for two phase flows of viscous imcompressible fluids.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、ax-lan k-
nstitutfurMathematik¨indenNaturwissenschaftenLeipzigDiffuseInterfaceModelsforTwo-PhaseFlowsofViscousIncompressibleFluids(revisedversion:February2008)byHelmutAbelsLecturenoteno.:362007DiffuseInterfaceModelsforTwo-PhaseFlowsofViscousIncompressibleFluidsHelmutAbelsFebruary1,20082Contents1

2、Introduction11.1ClassicalSharpInterfaceModel.....................11.2DiffuseInterfaceModelforMatchedDensities.............51.3DiffuseInterfaceModelforGeneralDensities..............101.4OverviewoftheAnalyticalResults...................122DerivationoftheDiffuseInterfaceModel152.1FundamentalQuantities

3、andEquations.................152.2LocalDissipationInequality.......................182.3ReformulationoftheSystem.......................222.4SimpleMixturesandConsequences...................233MathematicalBackground273.1Notation..................................273.2SomeResultsfromFunctionalAnalys

4、is.................273.3InterpolationSpaces...........................313.4FunctionSpacesonDomains.......................333.5SomeInequalitiesandProductEstimates................403.6NeumannLaplaceEquationandHelmholtzDecomposition......423.7Vector-ValuedFunctionSpacesandRealInterpolation........4

5、63.8SomeResultsRelatedtoWeakandStrongConvergence........493.9LinearEvolutionEquation.......................503.10MonotoneOperatorsandSubgradients.................523.11EvolutionEquationsforSubgradients..................553.12SubgradientsRelatedtotheFreeEnergy................574Cahn-HilliardEquat

6、ionwithConvection674.1ExistenceandRegularityTheory....................674.2DoubleObstacleLimit..........................754.3Lojasiewicz-SimonInequality......................775Navier-StokesSystemwithVariableViscosity795.1WeakSolutionsoftheNon-StationaryStokesSystem.........793CONTENTSi5.2Statio

7、naryStokesSystemandtheStokesOperator..........815.3MaximalRegularityfortheInstationaryStokesSystem.......915.4StrongSolutionstotheNavier-StokesSystem.............946MatchedDensities996.1MainResults...........................