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May/June 2016 Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains
Reinhard Farwig, Veronika Rosteck
Adv. Differential Equations 21(5/6): 401-428 (May/June 2016).

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 ${\tilde{L}^q}(\Omega)$.

Citation

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Reinhard Farwig. Veronika Rosteck. "Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains." Adv. Differential Equations 21 (5/6) 401 - 428, May/June 2016.

Information

Published: May/June 2016
First available in Project Euclid: 9 March 2016

zbMATH: 1341.35098
MathSciNet: MR3473580

Subjects:
Primary: 35Q30, 47A10, 76D07

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 5/6 • May/June 2016
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