Asymptotic analysis of Leray solution for the incompressible NSE with damping

Abstract

In 2008, Cai and Jiu showed that the Cauchy problem of the Navier-Stokes equations, with damping α∣u∣β−1u\alpha {| u| }^{\beta -1}u for α>0\alpha \gt 0 and β≥1\beta \ge 1 has global weak solutions in L2(R3){L}^{2}\left({{\mathbb{R}}}^{3}). In this article, we study the uniqueness and the continuity in L2(R3){L}^{2}\left({{\mathbb{R}}}^{3}) of this global weak solution. We also prove the large time decay for this global solution for β≥103\beta \ge \frac{10}{3}.

Keywords

• navier-stokes equations
• friedrich method
• global weak solution
• primary 35-xx
• 35q30
• 76d05
• 76n10