Results indicate singularity formation in compressible MHD solutions with radial symmetry, suggesting critical dynamics in fluid flows.
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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Cai et al. (2026) studied this question.
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