The Baire category method for intermittent convex integration

We use a convex integration construction from \cite{ModenaSattig2020} in a Baire category argument to show that weak solutions to the transport equation with incompressible vector fields with Sobolev regularity are generic in the Baire category sense. Using the construction of \cite{BurczakModenaSzekelyhidi20} we prove an analog statement for the 3D Navier-Stokes equations.