  We introduce a search method for a new class of gravitational-wave signals,
namely long-duration O(hours - weeks) transients from spinning neutron stars.
We discuss the astrophysical motivation from glitch relaxation models and we
derive a rough estimate for the maximal expected signal strength based on the
superfluid excess rotational energy. The transient signal model considered here
extends the traditional class of infinite-duration continuous-wave signals by a
finite start-time and duration. We derive a multi-detector Bayes factor for
these signals in Gaussian noise using $\F$-statistic amplitude priors, which
simplifies the detection statistic and allows for an efficient implementation.
We consider both a fully coherent statistic, which is computationally limited
to directed searches for known pulsars, and a cheaper semi-coherent variant,
suitable for wide parameter-space searches for transients from unknown neutron
stars. We have tested our method by Monte-Carlo simulation, and we find that it
outperforms orthodox maximum-likelihood approaches both in sensitivity and in
parameter-estimation quality.
