一类扩散陀螺动力学模型的适定性
Well-Posedness of a Diffusive Gyrokinetic Model
摘要：
本文研究了一个描述托卡马克等离子体中心区离子分布的有限Larmor半径模型，它包含一个回旋动力学输运方程和一个电中性方程。由于最后一个方程没有提供足够的规则性的电势，我们介绍了一个简单的线性碰撞算子适用于有限拉莫尔半径近似。接下来，我们研究在垂直于磁场的方向上的二维动力学，并证明由于碰撞和陀螺平均的平滑效应的整体存在的解决方案，以及短时间的唯一性和稳定性。
英文摘要：
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.
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