This book is an exposition of a new approach to the Navier-Stokes equations, using powerful techniques provided by nonstandard analysis, as developed by the authors. The topics studied include the existence and uniqueness of weak solutions, statistical solutions and the solution of general stochastic equations.The authors provide a self-contained introduction to nonstandard analysis, designed with applied mathematicians in mind and concentrated specifically on techniques applicable to the Navier-Stokes equations. The subsequent exposition shows how these new techniques allow a quick and intuitive entrance into the mathematical theory of hydrodynamics, as well as provide a research tool that has proven useful in solving open problems concerning stochastic equations.
- 246 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Nonstandard Methods For Stochastic Fluid Mechanics
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Table of contents
- Contents
- Preface
- Nonstandard Methodology
- Results
- Chapter 1 Standard Preliminaries
- Chapter 2 Nonstandard Preliminaries
- Chapter 3 Loeb Measure and Integration Theory
- Chapter 4 Weak Solutions of Navier-Stokes Equations
- Chapter 5 Statistical Solutions of Navier-Stokes Equations
- Chapter 6 Stochastic Navier-Stokes Equations
- Chapter 7 Statistical Solutions of Stochastic Navier-Stokes Equations
- Chapter 8 The Euler Equation
- Appendix: The Nonstandard Universe and the Transfer Principle
- Bibliography
- Notation
- Index
- Series on Advances in Mathematics for Applied Sciences
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Yes, you can access Nonstandard Methods For Stochastic Fluid Mechanics by Marek Capinski, Nigel J Cutland in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over 1.5 million books available in our catalogue for you to explore.