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Tables of Contents for Vorticity and Incompressible Fluid Flow
Chapter/Section Title
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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.