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March 10, 2026Mathematical Methods in the Applied Sciences0 citations

Singularity Formation to the Radial Symmetric Compressible MHD Equations

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LCLv CaiMYManwai YuenHZHongjie Zhao

Key Points

  • This research aims to investigate how classical solutions to radial symmetric compressible MHD equations develop singularities in finite time.
  • Analyzed the compressible magnetohydrodynamic equations in two and three dimensions.
  • Assumed initial conditions with radial symmetry and vanishing sound speed at the origin.
  • Explored the formation of singularities under ideal fluid flow conditions.
  • Classical solutions to the MHD equations develop singularities in finite time.
  • The presence of radial symmetry and vanishing initial sound speed contributes to this outcome.

Abstract

ABSTRACT This paper presents two results concerning the finite‐time singularity formation of solutions to the compressible magnetohydrodynamic (short for MHD) equations in two and three spatial dimensions for ideal fluid flows. Assuming the initial velocity and magnetic fields are radial symmetric, and the initial sound speed vanishes at the origin, we show that the classical solutions to the MHD system in will develop singularities in finite time.

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Cite This Study

Cai et al. (2026) studied this question.

synapsesocial.com/papers/69af94fa70916d39fea4c221https://doi.org/10.1002/mma.70632
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