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arXiv · 0803.2057

A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

Roman Shvydkoy
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Abstract

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3L^{9/2}$ and $\n u$ belongs to $L^3L^{9/5}$ localy away from a 1/2-Hölder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.

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Roman Shvydkoy. 2008-03-13. A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation. https://doi.org/10.1007/s10884-008-9124-3

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