On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces

Wisam Alame

Banach Center Publications (2005)

  • Volume: 70, Issue: 1, page 21-49
  • ISSN: 0137-6934

Abstract

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We prove the existence of solutions to the evolutionary Stokes system in a bounded domain Ω ⊂ ℝ³. The main result shows that the velocity belongs either to W p 2 s + 2 , s + 1 ( Ω T ) or to B p , q 2 s + 2 , s + 1 ( Ω T ) with p > 3 and s ∈ ℝ₊ ∪ 0. The proof is divided into two steps. First the existence in W p 2 k + 2 , k + 1 for k ∈ ℕ is proved. Next applying interpolation theory the existence in Besov spaces in a half space is shown. Finally the technique of regularizers implies the existence in a bounded domain. The result is generalized to the spaces W p 2 s , s ( Ω T ) and B p , q 2 s , s with p > 2 and s ∈ (1/2,1).

How to cite

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Wisam Alame. "On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces." Banach Center Publications 70.1 (2005): 21-49. <http://eudml.org/doc/281763>.

@article{WisamAlame2005,
abstract = {We prove the existence of solutions to the evolutionary Stokes system in a bounded domain Ω ⊂ ℝ³. The main result shows that the velocity belongs either to $W_p^\{2s+2,s+1\}(Ω^T)$ or to $B_\{p,q\}^\{2s+2,s+1\}(Ω^T)$ with p > 3 and s ∈ ℝ₊ ∪ 0. The proof is divided into two steps. First the existence in $W_p^\{2k+2,k+1\}$ for k ∈ ℕ is proved. Next applying interpolation theory the existence in Besov spaces in a half space is shown. Finally the technique of regularizers implies the existence in a bounded domain. The result is generalized to the spaces $W_p^\{2s,s\}(Ω^T)$ and $B_\{p,q\}^\{2s,s\}$ with p > 2 and s ∈ (1/2,1).},
author = {Wisam Alame},
journal = {Banach Center Publications},
keywords = {constant coefficients; existence; Stokes system; bounded domain; interpolation; regularizers},
language = {eng},
number = {1},
pages = {21-49},
title = {On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces},
url = {http://eudml.org/doc/281763},
volume = {70},
year = {2005},
}

TY - JOUR
AU - Wisam Alame
TI - On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces
JO - Banach Center Publications
PY - 2005
VL - 70
IS - 1
SP - 21
EP - 49
AB - We prove the existence of solutions to the evolutionary Stokes system in a bounded domain Ω ⊂ ℝ³. The main result shows that the velocity belongs either to $W_p^{2s+2,s+1}(Ω^T)$ or to $B_{p,q}^{2s+2,s+1}(Ω^T)$ with p > 3 and s ∈ ℝ₊ ∪ 0. The proof is divided into two steps. First the existence in $W_p^{2k+2,k+1}$ for k ∈ ℕ is proved. Next applying interpolation theory the existence in Besov spaces in a half space is shown. Finally the technique of regularizers implies the existence in a bounded domain. The result is generalized to the spaces $W_p^{2s,s}(Ω^T)$ and $B_{p,q}^{2s,s}$ with p > 2 and s ∈ (1/2,1).
LA - eng
KW - constant coefficients; existence; Stokes system; bounded domain; interpolation; regularizers
UR - http://eudml.org/doc/281763
ER -

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