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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
Author NameAffiliation
Qian Liu School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China 
Baoquan Yuan School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China 
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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.