Theory and Applications of Nonviscous Fluid Flows

1. Fluid Dynamic Limits of the Boltzmann Equation.- 1.1 The Boltzmann Equation.- 1.2 The Fluid Dynamic Limits.- 1.3 Comments.- 2. From Classical Continuum Theory to Euler Equations via N–S–F Equations.- 2.1 Newtonian Fluids.- 2.2 Partial Differential Equations for the Motion of Any Continuum.- 2.3 N–S–F Equations.- 2.4 Dimensionless N–S–F Equations.- 3. Short Presentation of Asymptotic Methods and Modelling.- 3.1 Method of Strained Coordinates.- 3.2 Method of Matched Asymptotic Expansions.- 3.3 Multiple Scale Method.- 3.4 Flow with Variable Viscosity: An Asymptotic Model.- 3.5 Low Mach Number Flows: Weakly Nonlinear Acoustic Waves.- 4. Various Forms of Euler Equations and Some Hydro-Aerodynamics Problems.- 4.1 Barotropic Inviscid Fluid Flow.- 4.2 Bernoulli Equation and Potential Flows.- 4.3 D’Alembert Paradox and Kutta–Joukowski–Villat Condition.- 4.4 Potential Flows and Water Waves.- 4.5 Compressible Eulerian Baroclinic Fluid Flow.- 4.6 Isochoric Fluid Flows.- 4.7 Isentropic Fluid Flow and the Steichen Equation.- 4.8 Steady Euler Equations and Stream Functions.- 5. Atmospheric Flow Equations and Lee Waves.- 5.1 Euler Equations for Atmospheric Motions.- 5.2 The Meteorological “Primitive” Kibel Equations.- 5.3 The Boussinesq Inviscid Equations.- 5.4 Isochoric Lee Waves.- 5.5 Boussinesq Lee Waves.- 6. Low Mach Number Flow and Acoustics Equations.- 6.1 Euler Incompressible Limit Equations.- 6.2 Equations of Acoustics.- 7. Turbo-Machinery Fluid Flow.- 7.1 Various Facets of an Asymptotic Theory.- 7.2 Through-Flow Model.- 7.3 Flow Analysis at the Leading/Trailing Edges of a Row.- 7.4 Complementary Remarks.- 8. Vortex Sheets and Shock Layer Phenomena.- 8.1 The Concept of Discontinuity.- 8.2 Jump Relations Associated with a Conservation Law.- 8.3 TheStructure of the Shock Layer.- 8.4 Some Properties of the Vortex Sheet.- 9. Rigorous Mathematical Results.- 9.1 Well-Posedness of Eulerian Fluid Flows.- 9.2 Existence, Regularity, and Uniqueness Results.- References.