GLOBAL WELL-POSEDNESS OF 3D INCOMPRESSIBLE HYPER-DISSIPATIVE HALL-MHD EQUATIONS IN ANISOTROPIC BESOV SPACES

doi:10.1007/s10473-025-0501-3

摘要/Abstract

摘要： In this paper, we investigate the well-posedness result of the three-dimensional incompressible hyper-dissipative Hall-Magnetohydrodynamic equations with small anisotropic derivative. Making using of anisotropic Littlewood-Paley theory, we conclude that the hyper-dissipative Hall-MHD system has a unique global solution provided that $$\begin{align*} \left(\|J_{0}\|_{\mathcal{B}^{1-2\alpha}_{2}}+\|(\Lambda_{h}^{-1}\partial_{3}u_{0}, B_{0}^{h})\|_{\mathcal{B}^{1-2\alpha}_{2}}\right) \cdot F(u_{0}, B_{0}) \end{align*}$$ is sufficiently small. Here, $F(u_{0}, B_{0})$ is a bounded function, which depends on $\|(u_{0}, B_{0})\|_{\mathcal{B}^{1-2\alpha}_{2}}$ and $\|u_{0}^{h}\|_{H^{1}}$.

关键词: hyper-dissipative Hall-MHD equations, global well-posedness, Littlewood-Paley theory

Abstract: In this paper, we investigate the well-posedness result of the three-dimensional incompressible hyper-dissipative Hall-Magnetohydrodynamic equations with small anisotropic derivative. Making using of anisotropic Littlewood-Paley theory, we conclude that the hyper-dissipative Hall-MHD system has a unique global solution provided that $$\begin{align*} \left(\|J_{0}\|_{\mathcal{B}^{1-2\alpha}_{2}}+\|(\Lambda_{h}^{-1}\partial_{3}u_{0}, B_{0}^{h})\|_{\mathcal{B}^{1-2\alpha}_{2}}\right) \cdot F(u_{0}, B_{0}) \end{align*}$$ is sufficiently small. Here, $F(u_{0}, B_{0})$ is a bounded function, which depends on $\|(u_{0}, B_{0})\|_{\mathcal{B}^{1-2\alpha}_{2}}$ and $\|u_{0}^{h}\|_{H^{1}}$.

Key words: hyper-dissipative Hall-MHD equations, global well-posedness, Littlewood-Paley theory

中图分类号:

35A01

Dezai MIN, Qingkai WANG, Gang WU, Zhuoya YAO. GLOBAL WELL-POSEDNESS OF 3D INCOMPRESSIBLE HYPER-DISSIPATIVE HALL-MHD EQUATIONS IN ANISOTROPIC BESOV SPACES[J]. 数学物理学报(英文版), 2025, 45(5): 1723-1751.

Dezai MIN, Qingkai WANG, Gang WU, Zhuoya YAO. GLOBAL WELL-POSEDNESS OF 3D INCOMPRESSIBLE HYPER-DISSIPATIVE HALL-MHD EQUATIONS IN ANISOTROPIC BESOV SPACES[J]. Acta mathematica scientia,Series B, 2025, 45(5): 1723-1751.

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