Electron. J. Differential Equations, Vol. 2026 (2026), No. 43, pp. 1-14.

Global well-posedness for 3D generalized magnetohydrodynamic equations in critical Fourier-Triebel-Lizorkin-Morrey spaces

Teng Ma, Lihui Guo

Abstract:
This article studies the Cauchy problem of the 3D generalized incompressible magnetohydrodynamic equations in critical Fourier-Triebel-Lizorkin-Morrey spaces. The introduction of the Fourier-Triebel-Lizorkin-Morrey spaces facilitates the estimation of nonlinear terms in the system via Fourier transforms. Moreover, the Fourier-Triebel-Lizorkin-Morrey spaces are strictly larger than the Fourier-Triebel-Lizorkin spaces. When the initial data are sufficiently small, the global well-posedness of solutions to the Cauchy problem for the 3D generalized incompressible magnetohydrodynamic equations is established using the Littlewood-Paley theory and the Banach-Picard contraction principle. Furthermore, we derive Gevrey-class regularity of the solutions in the Fourier-Triebel-Lizorkin-Morrey spaces.

Submitted March 15, 2026. Published June 23, 2026.
Math Subject Classifications: 35B40, 35Q86, 76D03, 76U05.
Key Words: Generalized incompressible magnetohydrodynamic equations; Littlewood-Paley theory; global well-posedness; Fourier-Triebel-Lizorkin-Morrey spaces; Gevrey-class regularity.
DOI: 10.58997/ejde.2026.43

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Teng Ma
College of Mathematics and System Science
Xinjiang University
Urumqi 830017, China
email: matengshuxue@163.com
Lihui Guo
College of Mathematics and System Science
Xinjiang University
Urumqi 830017, China
email: lihuiguo@xju.edu.cn

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