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Consider the instationary Stokes system in general unbounded domains Ω ⊂ Rn, n ≥ 2, with boundary of uniform class C3, and Navier slip or Robin boundary condition. The main result of this article is the maximal regularity of the Stokes operator in function spaces of the type L̃q de ned as Lq ∩ L2 when q ≥ 2, but as Lq + L2 when 1 < q < 2, adapted to the unboundedness of the domain.

Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains