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 consider the complex Ginzburg-Landau equation [] in Rn where []. We prove that negative energy solutions blow up in finite time if []. For a fixed initial value we obtain estimates of the blow-up time [] as []. It turns out that [] stays bounded (respectively, goes to infinity) as [] in the case where the solution of the limiting nonlinear Schrodinger equation blows up in finite time (respectively, is global). This is a joint work with Thierry Cazenave, from U. Paris VI, and Fred Weissler, from U. Paris XIII .