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.

The purpose of this book is to present a broad panorama of model problems encountered in nonviscous Newtonian fluid flows. This is achieved by investigating the significant features of the solutions of the corresponding equations using the method of asymptotic analysis. The book thereby fills a long-standing gap in the literature by providing researchers working on applied topics in hydro-aerodynamics, acoustics and geophysical fluid flows with exact results, without having to invoke the complex mathematical apparatus necessary to obtain those insights. The benefit of this approach is two-fold: outlining the idea of the mathematical proofs involved suggests methodologies and algorithms for numerical computation, and also often gives useful information regarding the qualitative behaviour of the solutions. This book is aimed at researchers and students alike as it also provides all the necessary basic knowledge about fluid dynamics.

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