#### Azzeddine El Baraka, Mohamed Toumlilin, The uniform global well-posedness and the stability of the 3D generalized magnetohydrodynamic equations with the Coriolis force, Vol. 2019 (2019), Article ID 12, pp. 1-15

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DOI: 10.23952/cot.2019.12

Received February 10, 2019; Accepted July 8, 2019; Published July 27, 2019

Abstract. This paper deals with the Cauchy problem of the 3D generalized magnetohydrodynamic equations with the Coriolis force (GMHDC). By using the Fourier localization argument and the Littlewood-Paley theory, we obtain the uniform global well-posedness results with small initial data $(u_{0}, b_{0})$ belonging to the critical Fourier-Besov-Morrey spaces $\mathcal{F\dot{N}}_{p,\lambda,q}^{4-2\alpha+\frac{\lambda-3}{p}}(\mathbb{R}^{3})$. Moreover, the stability of global solutions is also discussed.