Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system
Analysis of PDEs
2025-07-10 v1
Abstract
In this article, we consider the 3D-rotating magnetohydrodynamic (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables). We prove for weak and strong solutions, that the limit system, when the Rossby number goes to zero (i.-e. for strong rotation), is a 2D-MHD system with three components. Moreover we are able to provide explicit global-in-time convergence rates thanks to adapted Strichartz estimates and with the help of an additional 3D magnetic field transported by the 2D limit velocity.
Keywords
Cite
@article{arxiv.2507.06678,
title = {Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system},
author = {Frédéric Charve and Van-Sang Ngo},
journal= {arXiv preprint arXiv:2507.06678},
year = {2025}
}