Synopses & Reviews
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.
"This book is destined to become a classic...This is the standard to which the rest of us need to aspire." Journal of Fluid Mechanics
"There are about 11 books currently available on the market covering incompressible flows. Majda and Bertozzi's book is unique in covering both the classical and weak solutions for the incompressible and inviscid flows and is excellently done." Mathematical Reviews
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow.
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.