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Very weak solutions of the stationary Stokes equations in unbounded domains of half space type

Reinhard Farwig; Jonas Sauer

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 1, page 81-109
  • ISSN: 0862-7959

Abstract

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We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as ℝ + n , bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of ℝ + n , and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous Sobolev spaces. In addition to very weak solutions we also construct corresponding pressure functions in negative homogeneous Sobolev spaces.

How to cite

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Farwig, Reinhard, and Sauer, Jonas. "Very weak solutions of the stationary Stokes equations in unbounded domains of half space type." Mathematica Bohemica 140.1 (2015): 81-109. <http://eudml.org/doc/269886>.

@article{Farwig2015,
abstract = {We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as $\mathbb \{R\}^n_+$, bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of $\mathbb \{R\}^n_+$, and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous Sobolev spaces. In addition to very weak solutions we also construct corresponding pressure functions in negative homogeneous Sobolev spaces.},
author = {Farwig, Reinhard, Sauer, Jonas},
journal = {Mathematica Bohemica},
keywords = {Stokes equation; very weak solution; strong solution; domain of half space type},
language = {eng},
number = {1},
pages = {81-109},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Very weak solutions of the stationary Stokes equations in unbounded domains of half space type},
url = {http://eudml.org/doc/269886},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Farwig, Reinhard
AU - Sauer, Jonas
TI - Very weak solutions of the stationary Stokes equations in unbounded domains of half space type
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 1
SP - 81
EP - 109
AB - We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as $\mathbb {R}^n_+$, bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of $\mathbb {R}^n_+$, and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous Sobolev spaces. In addition to very weak solutions we also construct corresponding pressure functions in negative homogeneous Sobolev spaces.
LA - eng
KW - Stokes equation; very weak solution; strong solution; domain of half space type
UR - http://eudml.org/doc/269886
ER -

References

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