The Fourth Workshop on Fluids and PDE was held at the National Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, Brazil, from Monday 26 May to Friday 30 May 2014. This workshop is held every two to three years in Brazil. The fourth edition of the workshop was the closing event of a Thematic Program on Incompressible Fluids Dynamics, to be held at IMPA next Spring. Hence, the focus of the workshop will be incompressible fluid mechanics .

We will study the behavior of the solutions to the 2D Euler equations in a porous medium. In a first part, the porous medium will be composed of inclusions of size E separated by Eª and the fluid fills the exterior. We will compare the asymptotic solution with the solution to the 2D Euler equations in the full plane or outside an impermeable obstacle. In a second part, we will present another way to approximate an impermeable boundary: the vortex method, used in physics and engineering. The goal will be to justify rigorously this numerical method. These works are partially in collaboration with D. Arsenio, V. Bonnaillie-Noel, E. Dormy, M. Lopes Filho, N. Masmoudi, and H. Nussenzveig Lopes .