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The observed internal plateau of X-ray emission in some short GRBs suggeststhe formation of a remnant supra-massive magnetar following a double neutronstar (NS) merger. In this paper, we assume that the rotational energy is lostmainly via gravitational wave (GW) radiation instead of magnetic dipole (MD)radiation, and present further constraints on the NS nuclear equation of state(EoS) via mass quadrupole deformation and r-mode fluid oscillations of themagnetar. We present two short GRBs with measured redshifts, 101219A and160821B, whose X-ray light curves exhibit an internal plateau. This suggeststhat a supra-massive NS may survive as the central engine. By consideringtwelve NS EoSs, within the mass quadrupole deformation scenario we find thatthe GM1, DD2, and DDME2 models give an $M_{\rm p}$ band falling within the2$\sigma$ region of the proto-magnetar mass distribution for$\varepsilon=0.01$. This is consistent with the constraints from the MDradiation dominated model of rotational energy loss. However, for an r-modefluid oscillation model with $\alpha=0.1$ the data suggest that the NS EOS isclose to the Shen and APR models, which is obviously different from the MDradiation dominated and mass quadrupole deformation cases.

Constraining the nuclear equation of state via gravitational-wave radiation of short gamma-ray burst remnants