Abstract
This paper aims as the stability and large-time behavior of 3D incompressible magnetohydrodynamic (MHD) equations with fractional horizontal dissipation and magnetic diffusion. By using the energy methods, we obtain that if the initial data are small enough in \(H^3(\mathbb {R}^3)\), then this system possesses a global solution, and whose horizontal derivatives decay at least at the rate of \((1+t)^{-\frac{1}{2}}\). Moreover, if we control the initial data further small in \(H^3(\mathbb {R}^3)\cap H_h^{-1}(\mathbb {R}^3)\), the sharp decay of this solution and its first-order derivatives is established.
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Acknowledgements
The paper is supported by Natural Science Foundation of China (No. 11971200) and Ministry of Science and Technology of the People’s Republic of China (No. 2020YFA0712500).
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Li, J., Wang, H. & Zheng, D. Stability and sharp decay for 3D incompressible MHD system with fractional horizontal dissipation and magnetic diffusion. Z. Angew. Math. Phys. 74, 44 (2023). https://doi.org/10.1007/s00033-023-01939-5
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DOI: https://doi.org/10.1007/s00033-023-01939-5