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 present various results on the size of the nodal (zero) set for solutions of partial differential equations of elliptic and parabolic type. In particular, we establish a sharp upper bound for the (n - 1)-dimensional Hausdorff measure of the nodal sets of the eigenfunctions of regular analytic elliptic problems. We also show certain more recent results concerning semilinear equations (e.g., Navier-Stokes equations) and equations with non-analytic coefficients .