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 .

The radius of analyticity of the Navier-Stokes equations indicates a length scale below which viscous effects dominate the inertial ones, and in the context of 3D turbulence, it can be couched in terms of the so-called Kolmogorov length-scale, the unique length scale determined by the viscosity and energy dissipation rate alone. This talk will address a refinement of a semigroup approach initiated by [Biswas-Swanson '07] for obtaining a lower bound on this radius in terms of Gevrey norms of the initial data and forcing. This approach recovers the best-known estimate in 2D obtained by [Kukavica '98] on a significant portion of the attractor and in 3D by [Doering-Titi '95] on a significant portion of the weak attractor. Moreover, the method is elementary and robust, being easily applicable to a wide class of dissipative equations. .