  We study the dynamics of open charm production and the dilepton radiation of
the semi-leptonic decays of correlated $D\bar D$ pairs versus the quark-gluon
plasma (QGP) radiation and hadronic sources in relativistic heavy-ion
collisions. Our study is based on the Parton-Hadron-String Dynamics (PHSD)
transport approach employing a non-perturbative QCD description of the strongly
interacting quark-gluon plasma (sQGP) in terms of dynamical quasiparticles and
the EoS based on lattice QCD. We compare the PHSD results for charm observables
with the calculations from BAMPS (Boltzmann Approach to Multi-Parton
Scatterings) which is based on perturbative QCD with massless partons and
interaction cross sections calculated in leading order of the QCD coupling. We
compare the $p_T$ dependence of the ratio $R_{AA}$ of $D$-mesons in $A+A$ over
$p+p$ collisions scaled by the number of binary collisions $N_{bin}$ as well as
the elliptic flow $v_2$ of $D$-mesons calculated within the PHSD and BAMPS at
LHC energies. In other study, based on the PHSD calculations we find that the
dileptons from correlated $D-$meson semi-leptonic decays dominate the 'thermal'
radiation from the QGP in central Pb+Pb collisions at the intermediate masses
($1.2 < M < 3$ GeV) for higher invariant energies However, for invariant
energies $\sqrt{s_{NN}} < 40$ GeV the QGP radiation overshines the contribution
from $D,{\bar D}$ decays such that one should observe a rather clear signal
from the partonic dilepton radiation. This finding provides promising
perspectives to measure the QGP radiation in the dilepton experiments at RHIC
BES and the future FAIR/NICA facilities.
