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

• Autorzy: Wisam Alame
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 76D07: Stokes and related (Oseen, etc.) flows
• 35E99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 70
• Numer: 1
• Strony: 21-49

Daty

wydano

2005

Twórcy

autor

Wisam Alame

• Technical University of Warsaw, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc70-0-2