Epochs of regularity for weak solutions of the Navier-Stokes equations in unbounded domains (Q909114)

\textit{J. Leray} [Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63, 193-248 (1934)] proved the existence of weak solutions of the Navier-Stokes problem \[ u_ t+u\cdot \nabla u=-\nabla p+\Delta u+f\quad in\quad \Omega \times (0,\infty), \] \[ \nabla \cdot u=0\quad in\quad \Omega \times (0,\infty),\quad u|_{t=0}=a,\quad u|_{\partial \Omega}=0,\quad u(t)\in J_ 1(\Omega),\quad t>0 \] in the whole space \(R^ 3\). This paper in question presents an alternative argument, proving for the first time the existence of weak solutions possessing the epochs of regularity property in unbounded domain other than \(R^ 3\).