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 .

In this talk, we will discuss recent work which is joint with Wendong Wang and ZhoupingXin. It is shown here that suitable weak solutions to the 6D steady incompressible Navier-Stokes equations are Holder continuous near the boundary provided that either [formula] or [formula] is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points near the boundary is zero. This generalizes interior regularity results by Dong-Strain. .