Fluids under pressure Primitive Equations for Oceanic and Atmospheric Dynamics Viscous Compressible Flows under Pressure Global Well posedness for Incompressible Incompressible Two Phase Problem The Role of Pressure in the Theory of Weak Solutions to the Navier Stokes Equations Pressure Dependent Material Coefficients FE Pressure Stabilizations for Incompressible Flow Problems Finite Volume Methods for Navier Stokes Equations. This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure ” held in Prague as part of the “Prague Sum” series. Written by experts in their respective fields chapters explore the complex role that pressure plays in physics mathematical modeling and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well posedness of the Navier Stokes equations Weak solutions to the Navier Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.