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| Well-Posedness of MHD Equations in Sobolev-Gevery Space |
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| KeyWord:MHD equation, Sobolev-Gevery space, well-posedness |
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| Abstract: |
| This paper is devoted to the study of the 3D incompressible magnetohydrodynamic system. We prove the local in time well-posedness for any large initial data in $\dot{H}_{a,1}^{1}({\mathbb{R}}^{3})$ or $H_{a,1}^{1}({\mathbb{R}}^{3})$. Furthermore, the global well-posedness of a strong solution in $\tilde{L}^{\infty}(0,T;H_{a,1}^{1}({\mathbb{R}}^{3}))\cap L^{2}(0,T;\dot{H}_{a,1}^{1}({\mathbb{R}}^{3})\cap \dot{H}_{a,1}^{2}({\mathbb{R}}^{3}))$ with initial data satisfying a smallness condition is established. |
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