# On the gevrey regularity of solutions to the 3d ideal mhd equations

## TL;DR

This paper proves that solutions to the 3D ideal MHD equations maintain their Gevrey regularity over time, providing uniform estimates of the Gevrey radius, similar to results known for the Euler equations.

## Contribution

It establishes the propagation of Gevrey regularity for 3D ideal MHD solutions and provides uniform Gevrey radius estimates, extending regularity results to magnetohydrodynamics.

## Key findings

- Propagation of Gevrey regularity is proven for 3D ideal MHD solutions.
- Uniform estimates of the Gevrey radius are obtained.
- Results are analogous to those for the incompressible Euler equations.

## Abstract

In this paper, similar to the incompressible Euler equation, we prove the propagation of the Gevrey regularity of solutions to the three-dimensional incompressible ideal magnetohydrodynamics (MHD) equations. We also obtain an uniform estimate of Gevery radius for the solution of MHD equation.