Abstract
In this paper we prove the existence and uniqueness of classical solution for a system of PDEs recently developed in Refs. 60, 8, 10 and 11 to modelize the nonlinear gyrokinetic turbulence in magnetized plasma. From the analytical and numerical point of view this model is very promising because it allows to recover kinetic features (wave–particle interaction, Landau resonance) of the dynamic flow with the complexity of a multi-fluid model. This model, called the gyro-water-bag model, is derived from two-phase space variable reductions of the Vlasov equation through the existence of two underlying invariants. The first one, the magnetic moment, is adiabatic and the second, a geometric invariant named "water-bag", is exact and is just the direct consequence of the Liouville theorem.
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