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

Wisam Alame

Wisam Alame

Banach Center Publications, Tome 68 (2005), p. 21-49 / Harvested from The Polish Digital Mathematics Library

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Résumé

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).

Publié le : 2005-01-01

Zbl 1101.35345

EUDML-ID : urn:eudml:doc:281763

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     author = {Wisam Alame},
     title = {On the existence of solutions for the nonstationary Stokes system with slip boundary conditions in general Sobolev-Slobodetskii and Besov spaces},
     journal = {Banach Center Publications},
     volume = {68},
     year = {2005},
     pages = {21-49},
     zbl = {1101.35345},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-2}
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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, Tome 68 (2005) pp. 21-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc70-0-2/