Rapid time-decay and net force to the obstacles by the Stokes flow in exterior domains

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10 Citations (Scopus)

Abstract

Consider the nonstationary Stokes equations in exterior domains Ω ⊂ ℝn (n ≥ 3) with the compact boundary ∂Ω. We show first that the solution u(t) decays like ∥u(t)∥r = O(t-n/2(1-1/r)) for all 1 < r ≤ ∞ as t → ∞. This decay rate n/2(1 - 1/r) is optimal in the sense that ∥u(t)∥r = o(t-n/2(1-1/r)) for some 1 < r ≤ ∞ as t → ∞ occurs if and only if the net force exerted by the fluid on ∂Ω is zero.

Original languageEnglish
Pages (from-to)709-730
Number of pages22
JournalMathematische Annalen
Volume320
Issue number4
DOIs
Publication statusPublished - 2001 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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