涡和不可压缩流

图书标准信息

• 作者 A.J.Majda、A.L.Bertozzi 编
• 出版社 世界图书出版公司
• 出版时间 2003-09
• 版次 1
• ISBN 9787506265539
• 定价 98.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 545页

【内容简介】

Vorticityisperhapsthemostimportantfacetofturbulentfluidflows.Thisbookisintendedtobeacomprehensiveintroductiontothemathematicaltheoryofvorticityandincompressibleflowrangingfromelementaryintroductorymaterialtocurrentresearchtopics.Althoughthecontentscenteronmathematicaltheory,manypartsofthebookshowcaseamodemappliedmathematicsinteractionamongrigorousmathematicaltheory,numerical,asymptotic,andqualitativesimplifiedmodeling,andphysicalphenomena.Theinterestedreadercanseemanyexamplesofthissymbioticinteractionthroughoutthehook,especiallyinChaps.4-9and13.Theauthorshopethatthispointofviewwillbeinterestingtomathematiciansaswellasotherscientistsandengineerswithinterestinthemathematicaltheoryofincompressibleflows.

【目录】

Preface
1AnIntroductiontoVortexDynamicsforIncompressibleFluidFlows
1.1TheEulerandtheNavier-StokesEquations
1.2SymmetryGroupsfortheEulerandtheNavier-StokesEquations
1.3ParticleTrajectories
1.4TheVorticity,aDeformationMatrix,andSomeElementaryExactSolutions
1.5SimpleExactSolutionswithConvection,VortexStretching,andDiffusion
1.6SomeRemarkablePropertiesoftheVorticityinIdealFluidFlows
1.7ConservedQuantitiesinIdealandViscousFluidFlows
1.8Leray''sFormulationofIncompressibleFlowsandHodge''sDecompositionofVectorFields
1.9Appendix
NotesforChapter1
ReferencesforChapter1

2TheVorfidty-StreamFormulationoftheEuierandtheNavier.StokesEquations
2.1TheVorticity-StreamFormulationfor2DFlows
2.2AGeneralMethodforConstructingExactSteadySolutionstothe2DEulerEquations
2.3SomeSpecial3DFlowswithNontrivialVortexDynamics
2.4TheVorticity-StreamFormulationfor3DFlows
2.5FormulationoftheEulerEquationasanIntegrodifferentialEquationfortheParticleTrajectories
NotesforChapter2
ReferencesforChapter2

3EnergyMethodsfortheEulerandtheNavier-StokesEquations
3.1EnergyMethods:ElementaryConcepts
3.2Local-in-TimeExistenceofSolutionsbyMeansofEnergyMethods
3.3AccumulationofVorticityandtheExistenceofSmoothSolutionsGloballyinTime
3.4Viscous-SplittingAlgorithmsfortheNavier-StokesEquation
3.5AppendixforChapter3
NotesforChapter3
ReferencesforChapter3

4TheParticle-TrajectoryMethodforExistenceandUniquenessofSolutionstotheEulerEquation
4.1TheLocal-in-TimeExistenceofInviscidSolutions
4.2LinkbetweenGlobal-in-TimeExistenceofSmoothSolutionsandtheAccumulationofVorticitythroughStretching
4.3GlobalExistenceof3DAxisymmetricFlowswithoutSwirl
4.4HigherRegularity
4.5AppendixesforChapter4
NotesforChapter4
ReferencesforChapter4

5TheSearchforSingularSolutionstothe3DEulerEquations
5.1TheInterplaybetweenMathematicalTheoryandNumericalComputationsintheSearchforSingularSolutions
5.2ASimple1DModelforthe3DVorticityEquation
5.3A2DModelforPotentialSingularityFormationin3DEulerEquations
5.4PotentialSingularitiesin3DAxisymmetricFlowswithSwirl
5.5Dothe3DEulerSolutionsBecomeSingularinFiniteTimesNotesforChapter5
ReferencesforChapter5

6ComputationalVortexMethods
6.1TheRandom-VortexMethodforViscousStrainedShearLayers
6.22DInviscidVortexMethods
6.33DInviscid-VortexMethods
6.4ConvergenceofInviscid-VortexMethods
6.5ComputationalPerformanceofthe2DInviscid-VortexMethodonaSimpleModelProblem
6.6TheRandom-VortexMethodinTwoDimensions
6.7AppendixforChapter6
NotesforChapter6
ReferencesforChapter6

7SimplifiedAsymptoticEquationsforSlenderVortexFilaments
7.1TheSelf-InductionApproximation,Hasimoto''sTransform,andtheNonlinearSchrodingerEquation
7.2SimplifiedAsymptoticEquationswithSelf-StretchforaSingleVortexFilament
7.3InteractingParallelVortexFilaments-PointVorticesinthePlane
7.4AsymptoticEquationsfortheInteractionofNearlyParallelVortexFilaments
7.5MathematicalandAppliedMathematicalProblemsRegardingAsymptoticVortexFilaments
NotesforChapter7
ReferencesforChapter7

8WeakSolutionstothe2DEulerEquationswithInitialVorticltyinL
8.1EllipticalVorticies
8.2WeakLSolutionstotheVorticityEquation
8.3VortexPatches
8.4AppendixforChapter8
NotesforChapter8
ReferencesforChapter8

9IntroductiontoVortexSheets,WeakSolutions,andApproximate-SolutionSequencesfortheEulerEquation
9.1WeakFormulationoftheEulerEquationinPrimitive-VariableForm
9.2ClassicalVortexSheetsandtheBirkhoff-RottEquation
9.3TheKelvin-HelmholtzInstability
9.4ComputingVortexSheets
9.5TheDevelopmentofOscillationsandConcentrations
NotesforChapter9
ReferencesforChapter9

10WeakSolutionsandSolutionSequencesinTwoDimensions
10.1Approximate-SolutionSequencesfortheEulerandtheNavier-StokesEquations
10.2ConvergenceResultsfor2DSequenceswithL1andLp
VorticityControl
NotesforChapter10
ReferencesforChapter10

11The2DEulerEquation:ConcentrationsandWeakSolutionswithVortex-SheetInitialData
11.1Weak-*andReducedDefectMeasures
11.2ExampleswithConcentration
11.3TheVorticityMaximalFunction:DecayRatesandStrongConvergence
11.4ExistenceofWeakSolutionswithVortex-SheetInitialDataofDistinguishedSign
NotesforChapter11
ReferencesforChapter11

12ReducedHansdorffDimension,Oscillations,andMeasure-ValuedSolutionsoftheEulerEquationsinTwoandThreeDimensions
12.1TheReducedHausdorffDimension
12.2OscillationsforApproximate-SolutionSequenceswithoutL1VorticityControl
12.3YoungMeasuresandMeasure-ValuedSolutionsoftheEulerEquations
12.4Measure-ValuedSolutionswithOscillationsandConcentrations
NotesforChapter12
ReferencesforChapter12

13TheVlasov-PoissonEquationsnsanAnalogytotheEulerEquationsfortheStudyofWeakSolutions
13.1TheAnalogybetweenthe2DEulerEquationsandthe1DVlasov-PoissonEquations
13.2TheSingle-Component1DVlasov-PoissonEquation
13.3TheTwo-ComponentVlasov-PoissonSystem
NoteforChapter13
ReferencesforChapter13
Index