This paper considers solutions $u_\alpha$ of the three-dimensional Navier--Stokes equations on periodic domains $Q_\alpha:=(-\alpha,\alpha)^3$ as domain size $\alpha\to\infty$, and compares them to same whole space. For compactly-supported initial data $u_\alpha^0\in H^1(Q_\alpha)$, an appropriate extension converges a solution $u$ ${\mathbb R}^3$, strongly in $L^r(0,T;H^1({\mathbb R}^3))$, $r\...
