  The Chapman-Enskog method, in combination with the quantum maximum entropy
principle, is applied to the Wigner equation in order to obtain quantum
Navier-Stokes equations for electrons in graphene in the isothermal case. The
derivation is based on the quantum version of the maximum entropy principle and
follows the lines of Ringhofer-Degond-M\'ehats' theory (J. Stat. Phys. 112,
2003 and Z. Angew. Math. Mech. 90, 2010). The model obtained in this way is
then semiclassically expanded up to $\mathcal{O}(\hbar^2)$.
