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Full Description
Theoretical and Computational Fluid Mechanics: Existence, Blowup and Discrete Exterior Calculus Problems, Volume II is self-contained, though it builds upon the work of the previous volume in providing a comprehensive introduction to the mathematical theory of incompressible flows, with a focus on the foundational structures, analytical techniques, and open problems associated with the Navier-Stokes equations. In this volume, emphasis is placed on the interplay between geometry, functional analysis, and partial differential equations that underpins much of modern fluid theory. As a reference or teaching supplement, the book is accessible to anyone with a basic level of understanding of fluid dynamics and yet still engaging for those of a deeper understanding. The book is aimed at theorists and applied mathematicians from a wide range of scientific fields, including the social, health, and physical sciences. It provides a step-by-step guide to the construction of solutions of both elementary and open problems of viscous and non-viscous models, and for the applications of such models for the functional analysis and real analysis of data.
Features
Offers a self-contained treatment that does not require a previous background in fluid dynamics
Suitable as a reference text for graduate students, researchers, and professionals, and could easily be used as a teaching resource
Provides various examples using Maple, Mathematica, and to a lesser extent MATLAB® programming languages.
Contents
Ch 1 More on Euler's Equations, Gas Dynamics and Boundary Layers Ch 2 Fixed Point Theory Ch 3 PNS: Existence of a Non-Cauchy sequence sending blowup points to infinity Ch 4 PNS-Relation between two-point and three-point correlation functions Ch 5 RANS and Turbulence Ch 6 The Cauchy Problem for the Abstract Navier Stokes Equations and Harmonic Analysis Tools Ch 7 Introduction to No finite time singularities for PNS Ch 8 Existence of solutions to 3D Periodic Navier-Stokes equations(PNS) Ch 9 Technical Heat transfer
and thermodynamics Concepts Ch 10 Introduction to Pulses, Waves and Locally Compact Spaces Ch 11 Helmholtz-Kelvin- Stokes Types of Invariants by Integration of Total Rotational Momentum Densities for Incompressible Flows and the Solution of the fourth Millennium Problem Ch 12 Application of Discrete Exterior Calculus to Fluid Mechanics Problems Ch A Computer Programs Index
