Blowup of classical solutions for two-dimensional transverse magnetohydrodynamic equations

In this paper, we investigate the blowup phenomenon of solutions for two-dimensional transverse magnetohydrodynamic (MHD) equations. By using the integration method, we first prove that the classical solutions for γ≥2 of the transverse MHD equations with the initial bounded region Ω(0) surrounded by vacuum will blow up in finite time. Furthermore, we also establish the finite-time singularity formation of the classical solutions for γ>1 to the transverse MHD equations with a class of non-vacuum initial values. Copyright © 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.