Stokes equations in asymptotically flat layers

Helmut Abels

Banach Center Publications (2005)

  • Volume: 70, Issue: 1, page 9-19
  • ISSN: 0137-6934

Abstract

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We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Ω ₀ = ℝ n - 1 × ( - 1 , 1 ) . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded H ∞ -calculus for the associated Stokes operator and some of its consequences, which also yields an application to a free boundary value problem.

How to cite

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Helmut Abels. "Stokes equations in asymptotically flat layers." Banach Center Publications 70.1 (2005): 9-19. <http://eudml.org/doc/282067>.

@article{HelmutAbels2005,
abstract = {We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer $Ω₀ = ℝ^\{n-1\} × (-1,1)$. Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded $H_∞$-calculus for the associated Stokes operator and some of its consequences, which also yields an application to a free boundary value problem.},
author = {Helmut Abels},
journal = {Banach Center Publications},
keywords = {generalized Stokes resolvent equations; non-slip boundary conditions; unique solvability; Stokes operator; free boundary value problem},
language = {eng},
number = {1},
pages = {9-19},
title = {Stokes equations in asymptotically flat layers},
url = {http://eudml.org/doc/282067},
volume = {70},
year = {2005},
}

TY - JOUR
AU - Helmut Abels
TI - Stokes equations in asymptotically flat layers
JO - Banach Center Publications
PY - 2005
VL - 70
IS - 1
SP - 9
EP - 19
AB - We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer $Ω₀ = ℝ^{n-1} × (-1,1)$. Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded $H_∞$-calculus for the associated Stokes operator and some of its consequences, which also yields an application to a free boundary value problem.
LA - eng
KW - generalized Stokes resolvent equations; non-slip boundary conditions; unique solvability; Stokes operator; free boundary value problem
UR - http://eudml.org/doc/282067
ER -

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