## Advances in Differential Equations

- Adv. Differential Equations
- Volume 21, Number 5/6 (2016), 401-428.

### Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains

Reinhard Farwig and Veronika Rosteck

#### Abstract

Consider the Stokes resolvent system in general unbounded domains $\Omega \subset {\mathbb{R}^n}$, $n\geq 2$, with boundary of uniform class $C^{3}$, and Navier slip boundary condition. The main result is the resolvent estimate 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. As a consequence, we get that the Stokes operator generates an analytic semigroup on a solenoidal subspace ${\tilde{L}^q}_\sigma(\Omega)$ of ${\tilde{L}^q}(\Omega)$.

#### Article information

**Source**

Adv. Differential Equations, Volume 21, Number 5/6 (2016), 401-428.

**Dates**

First available in Project Euclid: 9 March 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1457536496

**Mathematical Reviews number (MathSciNet)**

MR3473580

**Zentralblatt MATH identifier**

1341.35098

**Subjects**

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 47A10: Spectrum, resolvent 76D07: Stokes and related (Oseen, etc.) flows

#### Citation

Farwig, Reinhard; Rosteck, Veronika. Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains. Adv. Differential Equations 21 (2016), no. 5/6, 401--428. https://projecteuclid.org/euclid.ade/1457536496