具有相等德拜长度和拉莫尔半径的二维陀螺动力学模型的适定性
Well-posedness of a 2D gyrokinetic model with equal Debye length and Larmor radius
摘要：
我们在这里研究[Bostan-Finot-Hauray，CRAS，2016]中获得的2D陀螺动力学模型，当典型的拉莫尔半径为德拜长度的量级时，它自然地表现为有限拉莫尔半径区域中具有非常大的外部均匀磁场的Vlasov-Poisson系统的极限。我们表明，该系统的柯西问题是适定在一个合适的空间，提供的初始条件满足一个标准的一致衰减速度假设。我们的结果依赖于系统的两个解决方案之间的一阶Wasserstein距离的稳定性估计。该稳定性估计直接意味着柯西问题解的唯一性（在适当的空间中）。的稳定性估计的情况下，一个正规化的相互作用的扩展允许证明的解决方案的存在性，作为一个类似的系统与正规化的相互作用的解决方案的限制。
英文摘要：
We study here a 2D gyrokinetic model obtained in [Bostan-Finot-Hauray,CRAS,2016], which naturally appears as the limit of a Vlasov-Poisson system with a very large external uniform magnetic field in the finite Larmor radius regime, when the typical Larmor radius is of order of the Debye length. We show that the Cauchy problem for that system is well-posed in a suitable space, provided that the initial condition satisfies a standard uniform decay assumption in velocity. Our result relies on a stability estimate in Wasserstein distance of order one between two solutions of the system. That stability estimate directly implies the uniqueness (in an appropriate space) of solution to the Cauchy problem. An extension of the stability estimate to the case of a regularized interaction allows to prove the existence of solutions, as limits of solutions of a similar system with regularized interactions.
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