不可壓縮非粘性流的數(shù)學(xué)理論（影印版）

Preface
Chapter1
GeneralConsiderationsontheEulerEquation
1.1.TheEquationofMotionofanIdealIncompressibleFluid
1.2.VorticityandStreamFunction
1.3.ConservationLaws
1.4.PotentialandIrrotationalFlows
1.5.Comments
Appendix1.1(LiouvilleTheorem)
Appendix1.2(ADecompositionTheorem)
Appendix1.3(Kutta-JoukowskiTheoremandComplexPotentials)
Appendix1.4(d'AlembertParadox)
Exercises
Chapter2
ConstructionoftheSolutions
2.1.GeneralConsiderations
2.2.LagrangianRepresentationoftheVorticity
2.3.GlobalExistenceandUniquenessinTwoDimensions
2.4.RegularityPropertiesandClassicalSolutions
2.5.LocalExistenceandUniquenessinThreeDimensions
2.6.SomeHeuristicConsiderationsontheThree-Dimensional
Motion
2.7.Comments
Appendix2.1(IntegralInequalities)
Appendix2.2(SomeUsefulInequalities)
Appendix2.3(Quasi-LipschitzEstimate)
Appendix2.4(RegularityEstimates)
Exercises
Chapter3
StabilityofStationarySolutionsoftheEulerEquation
3.1.AShortReviewoftheStabilityConcept
3.2.SufficientConditionsfortheStabilityofStationarySolutions:
TheArnoldTheorems
3.3.StabilityinthePresenceofSymmetries
3.4.Instability
3.5.Comments
Exercises
Chapter4
TheVortexModel
4.1.HeuristicIntroduction
4.2.MotionofVorticesinthePlane
4.3.TheVortexMotioninthePresenceofBoundaries
4.4.ARigorousDerivationoftheVortexModel
4.5.Three-DimensionalModels
4.6.Comments
Exercises
Chapter5
ApproximationMethods
5.1.Introduction
5.2.SpectralMethods
5.3.VortexMethods
5.4.Comments
Appendix5.1(OnK-RDistance)
Exercises
Chapter6
EvolutionofDiscontinuities
6.1.VortexSheet
6.2.ExistenceandBehavioroftheSolutions
6.3.Comments
6.4.SpatiallyInhomogeneousFluids
6.5.WaterWaves
6.6.Approximations
Appendix6.1(ProofofaTheoremoftheCauchy-KowalevskiType)
Appendix6.2(OnSurfaceTension)
Chapter7
Turbulence
7.1.Introduction
7.2.TheOnsetofTurbulence
7.3.PhenomenologicalTheories
7.4.StatisticalSolutionsandInvariantMeasures
7.5.StatisticalMechanicsofVortexSystems
7.6.Three-DimensionalModelsforTurbulence
References
Index