The Baire category method for intermittent convex integration

We use a convex integration construction from [22] in a Bairecategory argument to show that weak solutions to the transport equation withincompressible vector fields with Sobolev regularity are generic in the Baire categorysense. Using the construction of [7] we prove an analog statement for the3D Navier-Stokes equations.

Automated summary

In this paper, we use a convex integration construction and a Baire category argument to prove that weak solutions to the transport equation within compressible vector fields with Sobolev regularity are generic in the Baire category sense. We also prove a similar statement for the 3D Navier-Stokes equations using the construction method from reference [7].