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A Certain Necessary Condition of Potential Blow up for Navier-Stokes Equations

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Abstract

We show that a necessary condition for T to be a potential blow up time is \({\lim\nolimits_{t\uparrow T} \|v(\cdot,t)\|_{L_3}=\infty}\).

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Authors and Affiliations

  1. OxPDE, Mathematical Institute, University of Oxford, Oxford, UK

    G. Seregin

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  1. G. Seregin
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Correspondence to G. Seregin.

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Communicated by P. Constantin

On leave from St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia.

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Seregin, G. A Certain Necessary Condition of Potential Blow up for Navier-Stokes Equations. Commun. Math. Phys. 312, 833–845 (2012). https://doi.org/10.1007/s00220-011-1391-x

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