Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data
Analysis of PDEs
2026-03-24 v1
Abstract
Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in . Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in .
Cite
@article{arxiv.2603.21800,
title = {Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data},
author = {Zipeng Chen and Song Liu and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2603.21800},
year = {2026}
}