SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1122-1167, January 2021.
We prove the existence and uniqueness of smooth solutions with large initial data for a system of equations modeling the interaction of short waves, governed by a nonlinear Schrödinger equation, and long waves, described by the equations of magnetohydrodynamics. In the model, the short waves propagate along the streamlines of the fluid flow. This is translated in the system by the fact that the nonlinear Schrödinger equation is set up on the Lagrangian coordinates of the fluid. This prompts the crucial problem of establishing the regularity of the Lagrangian transformation, which is an important achievement of this paper. The latter is also a decisive point for the local well-posedness. The system provides a simplified mathematical model for studying aurora type phenomena. We focus on the two-dimensional case with periodic boundary conditions.

中文翻译：

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具有2个环面中的Aurora类型现象的系统的大数据全局平滑解决方案

SIAM数学分析杂志，第53卷，第1期，第1122-1167页，2021年1月。
对于一个由非线性Schrödinger方程控制的短波和由磁流体动力学方程描述的长波相互作用的方程组系统，我们证明了具有大初始数据的光滑解的存在性和唯一性。在模型中，短波沿着流体流线传播。非线性Schrödinger方程是在流体的拉格朗日坐标上建立的，这在系统中得到了转化。这引发了建立拉格朗日变换正则性的关键问题，这是本文的重要成果。后者也是当地良好状况的决定性因素。该系统为研究极光类型现象提供了简化的数学模型。我们关注具有周期性边界条件的二维情况。