PreprintCC BY 4.0arXiv
Reconnection in 2D Inertial Magnetohydrodynamics
Abstract
We consider two-fluid equations of inertial magnetohydrodynamics in two spatial dimensions. These equations can be recast as the evolution of two active scalars, with fluid-like interaction kernels. The equations come in two flavors, left-handed and right-handed. They are conservative and have global unique solutions for both smooth initial data and for initial data in Yudovich class L1(ℝ2)∩ L∞(ℝ2). We prove that the inviscid limit holds in Yudovich class. We prove the persistence of C2,α regularity of patch boundaries through merger events for the left-handed equations. We finally show numerical examples of magnetic reconnection, validating known rigorous results and uncovering new cases.
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BibTeX
@misc{boubendir2026reconnection,
title = {{Reconnection in 2D Inertial Magnetohydrodynamics}},
author = {Lydia Boubendir and Peter Constantin and Hezekiah Grayer II and Zhongtian Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23494},
eprint = {2610.23494},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23494},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reconnection in 2D Inertial Magnetohydrodynamics
AU - Lydia Boubendir
AU - Peter Constantin
AU - Hezekiah Grayer II
AU - Zhongtian Hu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23494
UR - https://arxiv.org/abs/2610.23494
AB - We consider two-fluid equations of inertial magnetohydrodynamics in two spatial dimensions. These equations can be recast as the evolution of two active scalars, with fluid-like interaction kernels. The equations come in two flavors, left-handed and right-handed. They are conservative and have global unique solutions for both smooth initial data and for initial data in Yudovich class L^1(ℝ^2)∩ L^∞(ℝ^2). We prove that the inviscid limit holds in Yudovich class. We prove the persistence of C^2,α regularity of patch boundaries through merger events for the left-handed equations. We finally show numerical examples of magnetic reconnection, validating known rigorous results and uncovering new cases.
ER -