The Boundary Regularity of a Weak Solution of the Navier-Stokes Equation and its Connection to the Interior Regularity of Pressure

We assume that v is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of v near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of v.