A newly-born magnetar is thought to be central engine of some long gamma-ray bursts ( GRBs ) .
We investigate the evolution of the electromagnetic ( EM ) emission from the magnetic dipole ( MD ) radiation wind injected by spin-down of a newly-born magnetar via both quadrupole gravitational-wave ( GW ) and MD radiations .
We show that the EM luminosity evolves as L _ { em } \propto ( 1 + t / \tau _ { c } ) ^ { \alpha } , and \alpha is -1 and -2 in the GW and MD radiation dominated scenarios , respectively .
Transition from the GW to MD radiation dominated epoch may show up as a smooth break with slope changing from -1 to -2 .
If the magnetar collapses to a black hole before \tau _ { c } , the MD radiation should be shut down , then the EM light curve should be a plateau followed by a sharp drop .
The expected generic light curve in this paradigm is consistent with the canonical X-ray light curve of Swift long GRBs .
The X-ray emission of several long GRBs are identified and interpreted as magnetar spin-down via GW or MD , as well as constrain the physical parameters of magnetar .
The combination of MD emission and GRB afterglows may make the diversity of the observed X-ray light curves .
This may interpret the observed chromatic behaviors of the X-ray and optical afterglow light curves and the extremely low detection rate of a jet-like break in the X-ray afterglow light curves of long GRBs .