On upper and lower bounds of rates of decay for nonstationary Navier-Stokes flows in the whole space.
type: Item
instance of: scholarly article
title: On upper and lower bounds of rates of decay for nonstationary Navier-Stokes flows in the whole space.
zbMATH Open document ID: 1048.35063
author: Tetsuro Miyakawa
published in: Hiroshima Mathematical Journal
publication date: 2002-01-01T00:00:00Z
review text: The title problem is studied in \(\mathbb{R}^n\) in homogeneous Besov spaces modulo polynomials. The main result states that the solution \(u(t)\) for large time \(t\) satisfies the estimate \[ 0< c_q'\leq t^{{n\over 2}(1+{1\over n}-{1\over q})}\| u(t)\|_{L^q}\leq c_q \] with appropriate constants \(c_q\), \(c_q'\), if and only if the initial velocity satisfies some moment conditions (here \({n\over n+1}\leq q\leq\infty\) for strong solution, and \({n\over n+1}\leq q\leq 2\) or weak solution). This result is then applied to the flows with cyclic symmetry.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 1911557
zbMATH Keywords: homogeneous Besov spaces
zbMATH Keywords: flows with cyclic symmetry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1151007491
OpenAlex ID: W2159709148
Wikidata QID: Q128870502
DOI: 10.32917/HMJ/1151007491
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description: scientific article; zbMATH DE number 1911557