  In this paper, we study the long time asymptotic behavior for the Cauchy
problem of the Novikov equation with $3\times 3$ matrix spectral problem
\begin{align} &u_{t}-u_{txx}+4 u_{x}=3uu_xu_{xx}+u^2u_{xxx}, \nonumber &u(x,
0)=u_{0}(x),\nonumber \end{align} where $u_0(x)$ $u_0(x)\rightarrow \kappa>0, \
x\rightarrow \pm \infty$ and $u_0(x)-\kappa$ is assumed in the Schwarz space.
It is shown that the solution of the Cauchy problem can be characterized via a
Riemann-Hilbert problem in a new scale $(y,t)$ with
$$y=x-\int_{x}^{\infty}\left( (u-u_{xx}+1)^{2/3} -1\right) ds.$$ In different
space-time solitonic regions of $\xi=y/t\in (-\infty,-1/8)\cup(1,+\infty) $ and
$\xi \in(-1/8,1)$, we apply $\overline\partial$ steepest descent method to
obtain the different long time asymptotic expansions of the solution $u(y,t)$.
The corresponding residual error order is $\mathcal{O}(t^{-1+\rho})$ and
$\mathcal{O}(t^{-3/4})$ respectively from a $\overline\partial$-equation. Our
result implies that soliton resolution can be characterized with an
$N(\Lambda)$-soliton whose parameters are modulated by a sum of localized
soliton-soliton interactions as one moves through the regions.
