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

Abstract

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

arXiv admin note: substantial text overlap with arXiv:2201.08292