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

Banach Center Publications (2005)

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

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topWisam 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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