论文标题
二维陀螺仪模型具有相等的debye长度和Larmor半径的良好适合性
Well-posedness of a 2D gyrokinetic model with equal Debye length and Larmor radius
论文作者
论文摘要
我们在这里研究了[Bostan-Finot-Hauray，Cras，2016]中获得的2D旋转模型，该模型在典型的Larmor Radius中的vlasov-Poisson系统自然而然地显示为典型的Larmor Radius中，当时典型的Larmor Radius是Debye长度的序列。我们表明，该系统的库奇问题在合适的空间中得到了很好的范围，前提是初始条件满足了速度的标准均匀衰变假设。我们的结果依赖于系统两种解决方案之间的订单距离的稳定性估计值。该稳定性估计直接意味着库奇问题解决方案的独特性（在适当的空间中）。稳定性估计的扩展到正则相互作用的情况下，可以证明解决方案的存在，这是具有正则相互作用的类似系统的解决方案的限制。
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.
