Vorticity and incompressible flow

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.