  We semi-analytically investigate the post-merger evolution of the binary
quark star merger. The effective-one-body method is employed to estimate the
energy and angular momentum dissipation due to gravitational waves in the
inspiral phase. Three major mechanisms of energy and angular momentum
dissipation are considered in the post-merger phase: mass outflows, neutrinos,
and gravitational waves. The proportion of each mechanism could be determined
by baryon number, energy and angular momentum conservation laws as well as the
equilibrium model for rotating quark stars. Applying this analysis to the
GW170817 event suggests two important conclusions: 1) a remnant quark star
whose mass is smaller than the maximum mass of a uniformly rotating quark star
can collapse before its rotational energy is dissipated via electromagnetic
radiation (i.e., $\sim 100\,\mathrm{s}$) as the angular momentum left in the
remnant quark star might not be large enough to sustain the additional
self-gravity of the supramassive quark star due to the angular momentum
dissipation of mass outflows, neutrinos and gravitational waves; 2) considering
a general quark star equation of state model, a constraint on the maximum mass
of cold and non-rotating quark stars is found as
$M_{\mathrm{TOV}}\lesssim2.35^{+0.07}_{-0.17}\,M_{\odot}$, assuming a delayed
collapse occurred before a large fraction of the total rotational energy
($\color{blue} \gtrsim 10^{53}\,$erg) of the merger remnant was deposited into
the merger environment for the GW170817 event. These constraints could be
improved with future merger events, once there are more evidences on its
post-merger evolution channel or information on the amount of post-merger
gravitational wave and neutrino emissions inferred from the multi-messenger
observations.
