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A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

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    0440826 - MÚ 2015 RIV CZ eng J - Journal Article
    Neustupa, Jiří
    A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations.
    Mathematica Bohemica. Roč. 139, č. 4 (2014), s. 685-698. ISSN 0862-7959
    R&D Projects: GA ČR GA13-00522S
    Institutional support: RVO:67985840
    Keywords : Navier-Stokes equation * suitable weak solution * regularity
    Subject RIV: BA - General Mathematics
    http://hdl.handle.net/10338.dmlcz/144145

    We deal with a suitable weak solution $(bold v,p)$ to the Navier-Stokes equations in a domain $Omegasubsetmathbb R^3$. We refine the criterion for the local regularity of this solution at the point $(bold fx_0,t_0)$, which uses the $L^3$-norm of $bold v$ and the $L^{3/2}$-norm of $p$ in a shrinking backward parabolic neighbourhood of $(bold x_0,t_0)$. The refinement consists in the fact that only the values of $bold v$, respectively $p$, in the exterior of a space-time paraboloid with vertex at $(bold x_0,t_0)$, respectively in a "small" subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point $(bold x_0,t_0)$ if $bold v$ and $p$ are "smooth" outside the paraboloid.
    Permanent Link: http://hdl.handle.net/11104/0243928
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