An $L^{q}(L²)$-theory of the generalized Stokes resolvent system in infinite cylinders

• Autorzy: Reinhard Farwig , Myong-Hwan Ri
• Języki publikacji: EN

Abstrakty

EN

Estimates of the generalized Stokes resolvent system, i.e. with prescribed divergence, in an infinite cylinder Ω = Σ × ℝ with $Σ ⊂ ℝ^{n-1}$, a bounded domain of class $C^{1,1}$, are obtained in the space $L^{q}(ℝ;L²(Σ))$, q ∈ (1,∞). As a preparation, spectral decompositions of vector-valued homogeneous Sobolev spaces are studied. The main theorem is proved using the techniques of Schauder decompositions, operator-valued multiplier functions and R-boundedness of operator families.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 42A45: Multipliers
• 76D07: Stokes and related (Oseen, etc.) flows
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 3
• Strony: 197-216

Daty

wydano

2007

Twórcy

autor

Reinhard Farwig

• Department of Mathematics, Darmstadt University of Technology, 64289 Darmstadt, Germany

autor

Myong-Hwan Ri

• Institute of Mathematics, Academy of Sciences, Pyongyang, DPR Korea

Identyfikatory

DOI

10.4064/sm178-3-1