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

```@article{Farwig2019MaximalRO,
title={Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains},
author={Reinhard Farwig and Veronika Rosteck},
journal={Journal of the Mathematical Society of Japan},
year={2019}
}```
• Published 1 October 2019
• Mathematics
• Journal of the Mathematical Society of Japan
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.
1 Citations

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## References

SHOWING 1-10 OF 38 REFERENCES
On the Stokes operator in general unbounded domains
• Mathematics
• 2009
It is known that the Stokes operator is not well-defined in L q -spaces for certain unbounded smooth domains unless q = 2. In this paper, we generalize a new approach to the Stokes resolvent problem
Stokes and Navier–Stokes Equations with Robin Boundary Conditions in a Half-Space
Abstract.We study the initial-boundary value problem for the Stokes equations with Robin boundary conditions in the half-space \$\$\mathbb{R}_ + ^n .\$\$ It is proved that the associated Stokes operator
On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain
We obtain the Lp–Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ℝn (n⩾2). The Robin condition consists of two conditions: v ⋅ u=0 and αu+β(T(u, p)v
Maximal Regularity of the Stokes Operator in General Unbounded Domains of ℝ n
• Mathematics
• 2007
It is well known that the Helmholtz decomposition of L q -spaces fails to exist for certain unbounded smooth domains unless q ≠ 2. Hence also the Stokes operator and the Stokes semigroup are not well
On the Lp-Lq maximal regularity of the Neumann problem for the Stokes equations in a bounded domain
• Mathematics
• 2008
Abstract In this paper, we prove the Lp-Lq maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a
The Stokes Resolvent Problem in General Unbounded Domains (Kyoto Conference on the Navier-Stokes Equations and their Applications)
• Mathematics, Philosophy
• 2007
It is well-known that the Helmholtz decomposition of Lq-spaces fails to exist for certain unbounded smooth domains unless q = 2. Hence also the Stokes operator is not well-defined for these domains
Stokes semigroups, strong,weak, and very weak solutions for general domains
• Mathematics
• 2018
To solve the (Navier-)Stokes equations in general smooth domains R, the spaces Q L. / defined asLq\L2 when 2 q <1 andLqCL2 when 1 < q < 2 have shown to be a successful strategy. First, the main
On the Helmholtz decomposition in general unbounded domains
• Mathematics
• 2007
Abstract.It is well known that the Helmholtz decomposition of Lq-spaces fails to exist for certain unbounded smooth planar domains unless q = 2, see [2], [9]. As recently shown [6], the Helmholtz
Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains
• Mathematics
• 2015
We consider weak solutions of the instationary Navier-Stokes system in general unbounded smooth domains \$\Omega\subset \mathbb{R}^3\$ and discuss several criteria to prove that the weak solution is
Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
• Mathematics
• 1986
SuntoSi studia la risolubilità e l'unicità inLp (1<p<+∞) della soluzione di problemi al contorno ellittici in domini illimitati la cui frontiera contiene un numero finito di punti angolosi.SummaryWe