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Well-posedness of a diffusive gyro-kinetic model. (English) Zbl 1269.82075

Summary: We study a finite Larmor radius model used to describe the ions distribution function in the core of a tokamak plasma, that consists in a gyro-kinetic transport equation coupled with an electro-neutrality equation. Since the last equation does not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. We next study the two-dimensional dynamics in the direction perpendicular to the magnetic field. Thanks to the smoothing effects of the collision and the gyro-average operators, we prove the global existence of solutions, as well as short time uniqueness and stability.

MSC:

82D75 Nuclear reactor theory; neutron transport
82D10 Statistical mechanics of plasmas
82C70 Transport processes in time-dependent statistical mechanics
78A35 Motion of charged particles
35Q82 PDEs in connection with statistical mechanics
35Q30 Navier-Stokes equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Software:

GYSELA
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Full Text: DOI

References:

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