Theoretical and Computational Fluid Mechanics: Existence, Blowup and Discrete Exterior Calculus Problems, Volume II(Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series)

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 as-sociated 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.

Table of 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

About the Author :
Terry E. Moschandreou has taught mathematics at the University of Western Ontario in the School of Mathematical and Statistical Sciences where he worked for several years. He received his PhD degree in Applied Mathematics from the University of Western Ontario in 1996. Keith Afas is a graduate researcher at the University of Western Ontario (UWO), who has been engaged in applied mathematics and mathematical modelling research since 2014, leading to multiple first-author and co-author publications, posters, conference presentations, and book chapters in a variety of topics. Khoa Nguyen has taught applied mathematics at Western University at London, Ontario, Canada since 2001 to present. Most of his students are engineering and science students. His interests are varying from physics to engineering, mathematics, and applications of mathematics to these fields. He has had two publications on Physical Review D with his collaborators and a book on numerical methods in C and Matlab with his colleague. He has a wife and two sons. They live in London, Ontario, Canada. Konstantinos E. Kyritsis is an associate professor at the University of Ioannina, Greece, affiliated with the School of Economics. Born in 1959 in Greece, he received his PhD in mathematics from the University of Athens in Greece, and he has worked at various other universities, like the University of Portsmouth in the UK. He has contributed to interdisciplinary research encompassing fields such as mathematics, physics, computer science, economics, philosophy, psychology, and music. He has proposed a solution for the 4th millennium problem about the Navier-Stokes equations and has applied the Navier-Stokes equations in understanding the renewable energy discovered by N. Tesla almost one century ago.