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

Abstract

Consider the instationary Stokes system in general unbounded domains Ω ⊂ ℝ^𝑛, 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 \tilde{𝐿}^𝑞 defined as 𝐿^𝑞 ∩ 𝐿² when 𝑞 ≥ 2, but as 𝐿^𝑞 + 𝐿² when 1 < 𝑞 < 2, adapted to the unboundedness of the domain.