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 .

I intend to show in several simple examples (with the use of Kato criteria and of dissipative solutions) how the introduction of the wild solutions of De Lellis and Szekelyhidi may contribute (if not to solutions) at least to the understanding of challenging problems posed by zero viscosity limit in presence of boundary or non regular initial data. This talk covers contributions done with Edriss Titi, Laszlo Szekelyhidi and Emil Wiedemann .