  We study the long-time asymptotic behavior of the focusing Fokas-Lenells (FL)
equation $$ u_{xt}+\alpha\beta^2u-2i\alpha\beta u_x-\alpha
u_{xx}-i\alpha\beta^2|u|^2u_x=0 \label{cs} $$ with generic initial data in a
Sobolev space which supports bright soliton solutions. The FL equation is an
integrable generalization of the well-known Schrodinger equation, and also
linked to the derivative Schrodinger model, but it exhibits several different
characteristics from theirs. (i) The Lax pair of the FL equation involves an
additional spectral singularity at $k=0$. (ii) four stationary phase points
will appear during asymptotic analysis, which require a more detailed necessary
description to obtain the long-time asymptotics of the focusing FL equation.
Based on the Riemann-Hilbert problem for the initial value problem of the
focusing FL equation, we show that inside any fixed time-spatial cone
$$\mathcal{C}\left(x_{1}, x_{2}, v_{1}, v_{2}\right)=\left\{(x, t) \in
\mathbb{R}^{2} | x=x_{0}+v t, x_{0} \in\left[x_{1}, x_{2}\right], v
\in\left[v_{1}, v_{2}\right]\right\},$$ the long-time asymptotic behavior of
the solution $u(x,t)$ for the focusing FL equation can be characterized with an
$N(\mathcal{I})$-soliton on discrete spectrums and a leading order term
$\mathcal{O}(|t|^{-1/2})$ on continuous spectrum up to a residual error order
$\mathcal{O}(|t|^{-3/4})$. The main tool is the $\overline{\partial}$ nonlinear
steepest descent method and the $\overline{\partial}$-analysis.
