Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations

Abstract

Any forward-in-time self-similar (localized-in-space) suitableweak solution to the 3D Navier-Stokes equations is shown to beinfinitely smooth in both space and time variables. As anapplication, a proof of infinite space and time regularity of aclass of a priori singular small self-similar solutionsin the critical weak Lebesgue space $L^{3,\infty}$ is given.