On the stability of global solutions to Navier--Stokes equations in the space
type: Item
instance of: scholarly article
title: On the stability of global solutions to Navier--Stokes equations in the space
zbMATH Open document ID: 1107.35096
author: Yanyan Li
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2004-11-23T00:00:00Z
review text: The authors consider the global solutions to Navier-Stokes equations in \(\mathbb R^3\) with data being a divergence-free vector-valued distribution. The solutions belong to the space defined by \textit{H. Koch} and \textit{D. Tataru} [Adv. Math. 157, No. 1, 22--35 (2001; Zbl 0972.35084)]. The authors show that the solutions are stable, in the sense that they vanish at infinity (in time), that they depend analytically on their data, and that the set of Cauchy data giving rise to such a solution is open in a specially defined topology. The proof relies on real variable energy estimates which the authors derive from the cancellation property of a trilinear form associated with Navier-Stokes equations.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 2118448
zbMATH Keywords: Navier--Stokes equations
zbMATH Keywords: asymptotics
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.matpur.2004.01.003
OpenAlex ID: W2052195558
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DOI: 10.1016/J.MATPUR.2004.01.003
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description: scientific article; zbMATH DE number 2118448