  Core-collapse supernovae are fascinating astrophysical objects for
multimessenger studies. Gravitational waves (GWs) are expected to play a role
in the supernova explosion mechanism, but their modelling is also challenging
due to the stochastic nature of the dynamics and the vast possible progenitors,
and moreover, the GW detection from these objects is still elusive with the
already advanced detectors. Low-energy neutrinos will be emitted enormously
during the core-collapse explosion and can help for the gravitational wave
counterpart search. In this work we develop a multi-messenger strategy to
search for such astrophysical objects by exploiting a global network of both
low-energy neutrino and gravitational wave detectors. First, we discuss how to
improve the detection potential of the neutrino sub-network by exploiting the
temporal behaviour of a neutrino burst from a core-collapse supernova. We show
that with the proposed approach neutrino detectors can gain at least $10\%$ of
detection efficiency at the distance where their efficiency drops. Then, we
combine the information provided by GW and neutrino in a multimessenger
strategy. In particular, we obtain an increase of the probability to detect the
GW signal from a CCSN at $60$ kpc from zero when using only GW analysis to
$\sim 33\%$ with our combined GW-$\nu$ approach.
  Keywords: multimessenger, supernova, core-collapse, low-energy neutrino,
gravitational wave.
