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In this work we characterise the performance of a new search techniquedesigned to be sensitive to the remnants of binary neutron star systems.Sensitivity estimates of the new method on simulated data are competitiveagainst those of other work. Previous searches for a gravitational-wave signalfrom a possible neutron star remnant of the binary neutron star merger eventGW170817 have focused on short ($<500$~s) and long duration (2.5~hr -- 8~day)signals. To date, no such post-merger signal has been detected. We introduce anew piecewise model which has the flexibility to accurately followgravitational-wave signals which are rapidly evolving in frequency, such asthose which may be emitted from young neutron stars born from binary neutronstar mergers or supernovae. We investigate the sensitivity and computationalcost of this piecewise model when used in a fully coherent 1800-second$\mathcal{F}$-statistic search on simulated data containing possible signalsfrom the GW170817 remnant. The sensitivity of the search using the piecewisemodel is determined using simulated data, with noise consistent with the LIGOsecond observing run. Across a 100--2000~Hz frequency band, the model achievesa peak sensitivity of $h_{\text{rss}}^{50\%} = 4.4 \times 10^{-23}\text{Hz}^{-1/2}$ at 200~Hz, competitive with other methods. The computationalcost of conducting the search, over a bank of $1.1 \times 10^{12}$ templates,is estimated at 10 days running on 100 CPU's.

Piecewise frequency model for searches for long-transient gravitational waves from young neutron stars