Well-Posedness of a Diffusive Gyrokinetic Model
Analysis of PDEs
2013-05-10 v1
Abstract
We study a finite Larmor radius model used to describe the ions distributions in the core of a toka-mak plasma, that consist in a gyro-kinetic transport equation, coupled with an electro-neutrality equation. Since the last equation do not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. Next we study the two-dimensional dynamics in the direction perpendicular to the magnetic field and prove thanks to the smoothing effects of the collisions and of the gyro-average the global existence of solutions, as well as short time uniqueness and stability.
Cite
@article{arxiv.1005.2104,
title = {Well-Posedness of a Diffusive Gyrokinetic Model},
author = {Maxime Hauray and Anne Nouri},
journal= {arXiv preprint arXiv:1005.2104},
year = {2013}
}