## 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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### References:

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