A Note on Prodi–Serrin Conditions for the Regularity of a Weak Solution to the Navier–Stokes Equations

The paper is concerned with the regularity of weak solutions to the Navier–Stokes equations. The aim is to show a relaxed Prodi–Serrin condition for regularity. The most interesting aspect of the result is that no compatibility condition is required on the initial data $$v_\circ \in J^2(\Omega )$$ .