  Several hydrodynamic descriptions of charge transport in graphene have been
presented in the late years. We discuss a general hydrodynamic model governing
the dynamics of a two-dimensional electron gas in a magnetized field-effect
transistor in the slow drift regime. The Dyakonov--Shur instability is
investigated including the effect of weak magnetic fields (i.e. away from
Landau levels). We show that the gap on the dispersion relation prevents the
instability to reach the lower frequencies thus imposing a limit on the Mach
number of the electronic flow. Furthermore, we discuss that the presence of the
external magnetic field decreases the growth rate of the instability, as well
as the saturation amplitude. The numerical results from our simulations and the
presented higher order dynamic mode decomposition support such reasoning.
