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Stokes resolvent systems in an infinite cylinder
Author(s) -
Farwig Reinhard,
Ri MyongHwan
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510536
Subject(s) - mathematics , resolvent , solenoidal vector field , bounded function , multiplier (economics) , mathematical analysis , domain (mathematical analysis) , fourier transform , cylinder , pure mathematics , vector field , geometry , economics , macroeconomics
In an infinite cylinder Ω = Σ × ℝ, where Σ ⊂ ℝ n –1 , n ≥ 3, is a bounded domain of C 1,1 class, we study the unique solvability of Stokes resolvent systems in L q (ℝ; L 2 (Σ)) for 1 < q < ∞ and in vector‐valued homogeneous Besov spaces (ℝ; L r (Σ)) for 1 ≤ p , q ≤ ∞, s ∈ ℝ, 1 < r < ∞. By a partial Fourier transform along the axis of the cylinder Ω the given system is reduced to a parametrized system on Σ, for which parameter independent estimates are proved. For further applications we obtain even parameter independent estimates in L r (Σ), 1 < r < ∞, in the non‐solenoidal case prescribing an arbitrary divergence g = div u . Then operator‐valued multiplier theorems are used for the final estimates of the Stokes resolvent systems in Ω. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)