English

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 BMO1BMO^{-1}. 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 BMO1(T5)BMO^{-1}(\mathbb{T}^5).

Keywords

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}
}