Consider a domain Ω ⊂ ℝn with possibly non compact but uniform C3-boundary and assume that the Helmholtz projection P exists on Lp(Ω) for some 1 p Lp(Ω) generates an analytic semigroup on admitting maximal Lq-Lp-regularity. Moreover, for there exists a unique local mild solution to the Navier–Stokes equations on domains of this form provided p > n.