  In this paper, we study the optimal time decay rate of isentropic
Navier-Stokes equations under the low regularity assumptions about initial
data. In the previous works about optimal time decay rate, the initial data
need to be small in $H^{[N/2]+2}(\mathbb{R}^{N})$. Our work combined negative
Besov space estimates and the conventional energy estimates in Besov space
framework which is developed by R. Danchin. Though our methods, we can get
optimal time decay rate with initial data just small in $\dot{B}^{N/2-1, N/2+1}
\cap \dot{B}^{N/2-1, N/2}$ and belong to some negative Besov space(need not to
be small). Finally, combining the recent results in \cite{zhang2014} with our
methods, we can only need the initial data to be small in homogeneous Besov
space $\dot{B}^{N/2-2, N/2} \cap \dot{B}^{N/2-1}$ to get the optimal time decay
rate in space $L^{2}$.
