Abstract
In these lectures we shall concentrate on some topics on the theory of incompressible fluids. In particular, we shall discuss the vorticity equations in 2D and 3D, the dynamic of point vertices, the bi-normal equation (modeling the motion of a self-interaction vortex filament), and the system for the interaction of nearly parallel vortex filaments deduced by Klein, Majda and Damodaran. We explain some of the results obtained by Kenig, Ponce and Vega concerning the existence of explicit solutions for this system as well as the stability of somespecial configurations.
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