  We present and analyze two mathematical models for the self consistent
quantum transport of electrons in a graphene layer. We treat two situations.
First, when the particles can move in all the plane $\RR^2$, the model takes
the form of a system of massless Dirac equations coupled together by a
selfconsistent potential, which is the trace in the plane of the graphene of
the 3D Poisson potential associated to surface densities. In this case, we
prove local in time existence and uniqueness of a solution in $H^s(\RR^2)$, for
$s > 3/8$ which includes in particular the energy space $H^{1/2}(\RR^2)$. The
main tools that enable to reach $s\in (3/8,1/2)$ are the dispersive Strichartz
estimates that we generalized here for mixed quantum states. Second, we
consider a situation where the particles are constrained in a regular bounded
domain $\Omega$. In order to take into account Dirichlet boundary conditions
which are not compatible with the Dirac Hamiltonian $H_{0}$, we propose a
different model built on a modified Hamiltonian displaying the same energy band
diagram as $H_{0}$ near the Dirac points. The well-posedness of the system in
this case is proved in $H^s_{A}$, the domain of the fractional order Dirichlet
Laplacian operator, for $1/2\leq s<5/2$.
