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arXiv · 2507.06678

Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system

Frédéric Charve·Van-Sang Ngo
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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.

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Frédéric Charve, Van-Sang Ngo. 2025-07-09. Mixed 3D-2D asymptotics for the weak and strong solutions of the rotating magnetohydrodynamic system. https://arxiv.org/abs/2507.06678

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