In recent times the hydrodynamic behaviour of electrons in graphene has attracted much interest from both the theoretical and experimental viewpoints. The usual approach to graphene hydrodynamics is  "semiclassical",  to the extent that the macroscopic equations are derived from a classical Boltzmann equation with conical momentum-energy relation. However, it would be interesting to obtain quantum corrections, similarly to what is done for traditional semiconductors, which can be achieved by using the quantum maximum entropy principle. However, due to the conical singular point, such procedure proves to be difficult in graphene and, so far, quantum corrections have been computed only for a regularized energy band. In the present work we show that singularities can actually be avoided, at least in the case of inviscid equations. [Il seminario si svolgerà all'interno delle attività del progetto PRIN 2022CHELC7 "Singular Interactions and Effective Models in Mathematical Physics" finanziato dall’Unione europea – Next Generation EU.]