Advances in Differential Equations

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

Reinhard Farwig and Veronika Rosteck

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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.


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