Uniqueness of almost periodic-in-time solutions to Navier–Stokes equations in unbounded domains

We present a uniqueness theorem for almost periodic-in-time solutions to the Navier–Stokes equations in 3-dimensional unbounded domains. Thus far, uniqueness of almost periodic-in-time solutions to the Navier–Stokes equations in unbounded domain, roughly speaking, is known only for a small almost pe...

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Bibliographic Details
Published in:Journal of evolution equations Vol. 11; no. 3; pp. 485 - 508
Main Authors: Farwig, Reinhard, Taniuchi, Yasushi
Format: Journal Article
Language:English
Published: Basel SP Birkhäuser Verlag Basel 01.09.2011
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Navier–Stokes equations
35Q35
Uniqueness
Unbounded domains
76D05
35Q30
Almost periodic solutions
ISSN:1424-3199, 1424-3202
Online Access:Get full text
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Summary:We present a uniqueness theorem for almost periodic-in-time solutions to the Navier–Stokes equations in 3-dimensional unbounded domains. Thus far, uniqueness of almost periodic-in-time solutions to the Navier–Stokes equations in unbounded domain, roughly speaking, is known only for a small almost periodic-in-time solution in within the class of solutions that have sufficiently small -norm. In this paper, we show that a small almost periodic-in-time solution in is unique within the class of all almost periodic-in-time solutions in . The proof of the present uniqueness theorem is based on the method of dual equations.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-010-0098-3