  Binary neutron star mergers are believed to eject significant masses with a
diverse range of velocities. Once these ejected materials begin to be
decelerated by a homogeneous medium, relativistic electrons are mainly cooled
down by synchrotron radiation, generating a multiwavelength long-lived
afterglow. Analytic and numerical methods illustrate that the outermost matter,
the merger shock-breakout material, can be parametrized by power-law velocity
distributions $\propto \left(\beta_{\rm c}\Gamma \right)^{-\alpha_s}$.
Considering that the shock-breakout material is moving on-axis towards the
observer and the relativistic jet off-axis, we compute the light curves during
the relativistic and the lateral expansion phase. As a particular case, we
successfully describe the X-ray, optical and radio light curves alongside the
spectral energy distribution from the recently discovered gravitational-wave
transient GW170817, when the merger shock-breakout material moves with mildly
relativistic velocities near-Newtonian phase and the jet with relativistic
velocities. Future electromagnetic counterpart observations of this binary
system could be able to evaluate different properties of these light curves.
