Affiliation:
1. Department of Mathematics, College of Sciences, King Saud University , Riyadh , Kingdom of Saudi Arabia
Abstract
Abstract
In 2008, Cai and Jiu showed that the Cauchy problem of the Navier-Stokes equations, with damping
α
∣
u
∣
β
−
1
u
\alpha {| u| }^{\beta -1}u
for
α
>
0
\alpha \gt 0
and
β
≥
1
\beta \ge 1
has global weak solutions in
L
2
(
R
3
)
{L}^{2}\left({{\mathbb{R}}}^{3})
. In this article, we study the uniqueness and the continuity in
L
2
(
R
3
)
{L}^{2}\left({{\mathbb{R}}}^{3})
of this global weak solution. We also prove the large time decay for this global solution for
β
≥
10
3
\beta \ge \frac{10}{3}
.