J. Nonl. Mod. Anal., 6 (2024), pp. 184-193.
Published online: 2024-03
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This paper devotes to consider the local existence of the strong solutions to the generalized MHD system with fractional dissipative terms $Λ^{2α}u$ for the velocity field and $Λ^{2α}b$ for the magnetic field, respectively. We construct the approximate solutions by the Fourier truncation method, and use energy method to obtain the local existence of strong solutions in $H^s (\mathbb{R}^n)$ $(s > max \{\frac{n}{2} + 1 − 2α, 0\})$ for any $α ≥ 0.$
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2024.184}, url = {http://global-sci.org/intro/article_detail/jnma/22974.html} }This paper devotes to consider the local existence of the strong solutions to the generalized MHD system with fractional dissipative terms $Λ^{2α}u$ for the velocity field and $Λ^{2α}b$ for the magnetic field, respectively. We construct the approximate solutions by the Fourier truncation method, and use energy method to obtain the local existence of strong solutions in $H^s (\mathbb{R}^n)$ $(s > max \{\frac{n}{2} + 1 − 2α, 0\})$ for any $α ≥ 0.$