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Solutions of the Navier-Stokes initial value problem in weighted Lq-spaces

✍ Scribed by Andreas Fröhlich

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
247 KB
Volume
269-270
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The problem of strong solvability of the nonstationary Navier‐Stokes equations is considered in weighted L^q^‐spaces L^q^~ω~(Ω), where the domain Ω ⊂ ℝ^n^ is the half space ℝ^n^~+~ or a bounded domain with boundary of class C^1,1^ and the weight ω belongs to the Muckenhoupt class A~q~. We give general conditions on the weight function ensuring the existence of a unique strong solution at least locally in time. In particular, these conditions admit weight functions ω ∈ A~q~, which become singular at the boundary or, in the case Ω = ℝ^n^~+~, grow for |x| →∞. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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