New blow-up criteria for local solutions of the 3D generalized MHD equations in Lei–Lin–Gevrey spaces |
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| Authors: | Wilberclay G Melo Natã Firmino Rocha |
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| Institution: | 1. Universidade Federal de Sergipe, Departamento de Matemática, São Cristóvão-SE, Brazil;2. Universidade Estadual do Piauí, Campus Clóvis Moura, Teresina-PI, Brazil |
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| Abstract: | This paper determines the existence of a unique local solution for the 3D generalized magnetohydrodynamics equations. In order to be more precise, our solution is obtained by involving Lei–Lin–Gevrey spaces as well as Lei–Lin spaces. Furthermore, we present five new blow-up criteria for this same system when the maximal time of existence is finite. It is important to point out that one of these criteria is obtained by assuming fractional Laplacians with equal powers. |
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| Keywords: | blow-up criteria generalized MHD equations Lei–Lin–Gevrey spaces local existence of solutions |
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