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Preprint, Working Paper, Document sans référence, etc. |
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| Titre : |
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Espaces critiques pour le système des equations de Navier-Stokes incompressibles |
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| Auteur(s) : |
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Pascal Auscher ( ) 1, Philippe Tchamitchian () 2 |
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| Laboratoire : |
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| Résumé : |
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In this work, we exhibit abstract conditions on a functional space E who insure the existence of a global mild solution for small data in E or the existence of a local mild solution in absence of size constraints for a class of semi-linear parabolic equations, which contains the incompressible Navier-Stokes system as a fundamental example. We also give an abstract criterion toward regularity of the obtained solutions. These conditions, given in terms of Littlewood-Paley estimates for products of spectrally localized elements of $E$, are simple to check in all known cases: Lebesgue, Lorents, Besov, Morrey... spaces. These conditions also apply to non-invariant spaces E and we give full details in the case of some 2-microlocal spaces. The following comments did not show on the first version: This article was written around 1998-99 and never published, because at that time, Koch and Tataru announced their result on well-posedness of Navier-stokes equations with initial data in $BMO^{-1}$. We believe though that some results and counterexamples here are of independent interest and we make them available electronically. |
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Langue du texte
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Français |
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Date de production,
écriture : |
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07/05/1999 |
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| Mots Clés : |
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Navier-Stokes systems – mild solutions – Littlewood-Paley decomposition – maximal spaces |
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| Classification : |
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AMS: 35K55, 35Q30, 35R05, 35S50, 42B25 |
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| Commentaire : |
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No modification to the text. This work was done when the first author was at Université de Picardie. |
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