The Cauchy problem for the time-dependent Bogoliubov-Dirac-Fock evolution of graphene has a unique global solution for Fermi velocities above a critical threshold.
Borrelli , Stationary solutions for the 2D critical Dirac equation wit h Kerr nonlinearity , Journal of Differential Equations, 263 (2017), pp
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Global well-posedness in a Hartree-Fock model for graphene
The Cauchy problem for the time-dependent Bogoliubov-Dirac-Fock evolution of graphene has a unique global solution for Fermi velocities above a critical threshold.