# Global smooth solutions with large data for a system modeling aurora type phenomena in the 2-torus

## TL;DR

This paper establishes the existence and uniqueness of smooth solutions with large initial data for a coupled nonlinear Schrödinger and magnetohydrodynamics system modeling aurora phenomena on a 2D torus, advancing understanding of complex wave-fluid interactions.

## Contribution

It provides the first proof of smooth solutions with large data for this multidimensional coupled system modeling aurora phenomena.

## Key findings

- Proved existence and uniqueness of solutions for large initial data.
- Established results specifically for the 2D periodic case.
- Advanced mathematical understanding of wave-fluid interaction models.

## Abstract

We prove 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 Schr\"odinger 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 setting up the nonlinear Schr\"odinger equation in the Lagrangian coordinates of the fluid. Besides, the equations are coupled by nonlinear terms accounting for the strong interaction of the dynamics. The system provides a simplified mathematical model for studying aurora type phenomena. We focus on the 2-dimensional case with periodic boundary conditions. This is the first result on existence of smooth solutions with large data for the multidimensional case of the model under consideration.