The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
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DOI：
10.1007/978-1-4614-6348-1_10
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
D. Lannes;F. Linares;J. Saut
中科院分区：
文献类型：
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作者：
D. Lannes;F. Linares;J. Saut
本文考虑了均匀磁化等离子体中由欧拉-泊松系统导出的Zakharov-Kuznetsov方程的严格证明。我们首先提供了一个证明的局部适定性的柯西问题的上述系统在二维和三维。证明了长波小振幅极限可用Zakharov-Kuznetsov方程描述。首先在冷等离子体的情况下，我们将展示如何扩展这一结果的等温压力项的存在下，统一的估计，当后者趋于零。
We consider in this paper the rigorous justification of the Zakharov–Kuznetsov equation from the Euler–Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave small-amplitude limit is described by the Zakharov–Kuznetsov equation. This is done first in the case of cold plasma; we then show how to extend this result in presence of the isothermal pressure term with uniform estimates when this latter goes to zero.