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Partial regularity of solutions to the fractional Navier-Stokes equations

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  • We study the partial regularity of suitable weak solutions to the Navier-Stokes equations with fractional dissipation $\sqrt{-\Delta}^s$ in the critical case of $s=\frac{3}{2}$. We show that the two dimensional Hausdorff measure of space-time singular set of these solutions is zero.
    Mathematics Subject Classification: Primary: 76D03, 76D05; Secondary: 35Q30.

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