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.
Synopsis:
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow.
Table of Contents
1. An introduction to vortex dynamics for incompressible fluid flows; 2. The vorticity-stream formulation for 2D flows; 3. Energy methods for the Euler and Navier-Stokes equations; 4. The particle trajectory method for existence and uniqueness of solutions to the Euler equation; 5. The search for singular solutions of the 3-D Euler equations; 6. Computational vortex methods; 7. Simplified asympototic equations for slender vortex filaments; 8. Weak solutions to the 2-D Euler equations with initial vorticity in L00; 9. Introduction to vortex sheets, weak solutions, and approximate solution sequences for the Euler equation; 10. Weak solutions and solution sequences in 2D; 11. The 2D Euler equation: concentrations and weak solutions with vortex sheet initial data; 12. Reduced Hausdorff oscillations, and measure valued solutions of the Euler equations in 2 and 3D; 13. The Vlasov-Poisson equations as an analogy to the Euler equations for the study of weak solutions.
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