The Stokes-system in exterior domains:Lp-estimates for small values of a resolvent parameter

  • Paul Deuring
Original Papers

Abstract

We consider the resolvent problem for the Stokes-system in an exterior domain:
$$- v \cdot \Delta u + \lambda \cdot u + \nabla \pi = f,divu = 0in\mathbb{R}^3 \backslash \bar \Omega ,$$
, with υε]0, ∞[, λεℂ] −∞, 0], Ω bounded domain in ℝ3, withC2-boundary ∂Ω. In addition, Dirichlet boundary conditionsu¦Ω=0 are prescribed. Using the method of integral equations, we estimate solutions (u,π) inLp-norms, for small values of ¦λ¦.

Zusammenfassung

Wir betrachten das Resolventenproblem zum Stokes-System im Außenraum:
$$- v \cdot \Delta u + \lambda \cdot u + \nabla \pi = f,divu = 0in\mathbb{R}^3 \backslash \bar \Omega ,$$
, Dabei ist Ω ein beschränktes Gebiet in ℝ3, mitC2-Berandung ∂Ω. Ferner ist υε]0, ∞[ und λεℂ] −∞, 0]. Zusätzlich verlangen wir, daßu die Randbedingungu¦Ω=0 erfüllt. Lösungen (u,π) dieses Problems schätzen wir inLp-Normen ab, wobei vorausgesetzt wird, daß ¦λ¦ klein ist.

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Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • Paul Deuring
    • 1
  1. 1.Fachbereich 4-MathematikTH DarmstadtDarmstadtFederal Republic of Germany

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