Vorticity and Incompressible Flow
This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
1116931145
Vorticity and Incompressible Flow
This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
191.0 In Stock
Vorticity and Incompressible Flow

Vorticity and Incompressible Flow

Vorticity and Incompressible Flow

Vorticity and Incompressible Flow

Overview

This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

Product Details

ISBN-13: 9780521630573
Publisher: Cambridge University Press
Publication date: 11/26/2001
Series: Cambridge Texts in Applied Mathematics , #27
Pages: 558
Product dimensions: 7.05(w) x 10.04(h) x 1.26(d)

Table of Contents

Preface; 1. An introduction to vortex dynamics for incompressible fluid flows; 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations; 3. Energy methods for the Euler and the Navier-Stokes equations; 4. The particle-trajectory method for existence and uniqueness of solutions to the Euler equation; 5. The search for singular solutions to the 3D Euler equations; 6. Computational vortex methods; 7. Simplified asympototic equations for slender vortex filaments; 8. Weak solutions to the 2D Euler equations with initial vorticity in L∞; 9. Introduction to vortex sheets, weak solutions and approximate-solution sequences for the Euler equation; 10. Weak solutions and solution sequences in two dimensions; 11. The 2D Euler equation: concentrations and weak solutions with vortex-sheet initial data; 12. Reduced Hausdorff dimension, oscillations and measure-valued solutions of the Euler equations in two and three dimensions; 13. The Vlasov-Poisson equations as an analogy to the Euler equations for the study of weak solutions; Index.
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