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- W2963734225 abstract "We study a weak stability problem for the three-dimensional Navier–Stokes system: if a sequence (u0,n)n∈N of initial data, bounded in some scaling invariant space, converges weakly to an initial data u0 which generates a global regular solution, does u0,n generate a global regular solution? Because of the invariances of the Navier–Stokes equations, a positive answer in general to this question would imply global regularity for any data, so we introduce a new concept of weak convergence (rescaled weak convergence) under which we are able to give a positive answer. The proof relies on profile decompositions in anisotropic spaces and their propagation by the Navier–Stokes equations. On étudie la stabilité faible pour le système de Navier–Stokes : si une suite de données de Cauchy (u0,n)n∈N, bornée dans un espace invariant par échelle, converge faiblement vers une donnée u0 engendrant une solution globale régulière, est-ce que u0,n engendre une solution globale régulière ? À cause des invariances de l'équation de Navier–Stokes, une réponse positive en toute généralité à cette question impliquerait la régularité globale pour toutes les données. Dans ce travail, nous fournissons une réponse positive dans le cadre d'un nouveau concept de convergence faible. La preuve est basée sur des décompositions en profils dans des espaces anisotropes et leur propagation par les équations de Navier–Stokes." @default.
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- W2963734225 date "2014-04-01" @default.
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- W2963734225 title "Stability by rescaled weak convergence for the Navier–Stokes equations" @default.
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- W2963734225 doi "https://doi.org/10.1016/j.crma.2014.02.007" @default.
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