Regularity via one vorticity component for the 3D axisymmetric MHD equations

Zhengguang Guo and Fangru Chen

Mathematische Nachrichten, 2023, vol. 296, issue 2, 675-688

Abstract: In this paper, we investigate the regularity criteria of axisymmetric weak solutions to the three‐dimensional (3D) incompressible magnetohydrodynamics (MHD) equations with nonzero swirl component. By making use of techniques of the Littlewood–Paley decomposition, we show that weak solutions to the 3D axisymmetric MHD equations become regular if the swirl component of vorticity satisfies that wθeθ∈L1(0,T;Ḃ∞,∞0)$w_{\theta }e_{\theta }\in L^{1}\big (0,T;\dot{B}_{\infty ,\infty }^{0}\big )$, which partially gives a positive answer to the marginal case for the regularity of MHD equations.

Date: 2023
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https://doi.org/10.1002/mana.202000419

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