Long Time Decay of Leray Solution of 3D-NSE With Damping

In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $α|u|^{β-1}u(α>0,\;β\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the continuity in $L^2$ for $β>3$, also the large time decay is proved for $β\geq\frac{10}3$. Fourier analysis and standard techniques are used.

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