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Suitable Solutions for the Navier–Stokes Problem with an Homogeneous Initial Value

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Abstract

This paper is devoted to the study of strong or weak solutions of the Navier–Stokes equations in the case of an homogeneous initial data. The case of small initial data is discussed. For large initial data, an approximation is developed, in the spirit of a paper of Vishik and Fursikov. Qualitative convergence is obtained by use of the theory of Muckenhoupt weights.

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Authors and Affiliations

  1. Équipe Analyse et Probabilités, EA2172, Université d’Evry Val d’Essonne, 91025, Evry cedex, France

    Pierre Gilles Lemarié–Rieusset & Frédéric Lelièvre

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  1. Pierre Gilles Lemarié–Rieusset
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  2. Frédéric Lelièvre
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Correspondence to Pierre Gilles Lemarié–Rieusset.

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Communicated by P. Constantin

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Lemarié–Rieusset, P.G., Lelièvre, F. Suitable Solutions for the Navier–Stokes Problem with an Homogeneous Initial Value. Commun. Math. Phys. 307, 133–156 (2011). https://doi.org/10.1007/s00220-011-1291-0

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  • DOI: https://doi.org/10.1007/s00220-011-1291-0

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