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 prove that particle paths are real analytic in well-posed hydrodynamic systems, once the velocity spatial gradient is Holder continuous. The proof addresses directly the combinatorial issues and then follows from a uniform arc chord condition by singular integral calculus. This is joint work with Vlad Vicol and Jiahong Wu .