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Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains. (English) Zbl 1434.35049

Summary: Consider the instationary Stokes system in general unbounded domains \(\Omega \subset \mathbb{R}^n, n \geq 2\), with boundary of uniform class \(C^3\), 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 \(L^q \cap L^2\) when \(q \geq 2\), but as \(L^q + L^2\) when \(1 < q < 2\), adapted to the unboundedness of the domain.

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
76D07 Stokes and related (Oseen, etc.) flows
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