The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure. (Q851601)

In this paper the author deals with a weak solution \({\mathbf v}\) to the non-steady Navier-Stokes equations in a bounded domain \(\Omega \) that satisfies the strong energy inequality. The author assumes that conditions of the Prodi-Serrin type are satisfied in a certain neighbourhood of the boundary. He shows the consequence for the regularity of \({\mathbf v}\) near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of \({\mathbf v}\). In order to prove this results the author uses fine properties of the Stokes operator A, which is selfadjoint and positive in \(L^2_{\sigma }(\Omega )^3\).