On existence of solutions for the nonstationary Stokes system with boundary slip conditions

• Autorzy: Wisam Alame
• Języki publikacji: EN

Abstrakty

EN

Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to $W_p^{2,1}(Ω × (0,T))$, and pressure belongs to $W_p^{1,0}(Ω × (0,T))$ for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing initial data is considered.

Kategorie tematyczne

• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2005
• Tom: 32
• Numer: 2
• Strony: 195-223

Daty

wydano

2005

Twórcy

autor

Wisam Alame

• Faculty of Mathematics, and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/am32-2-7