Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations |
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Authors: | Yongjiang Yu Kaitai Li |
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Affiliation: | a Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China b Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China |
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Abstract: | In this paper we derive some new equations and we call them MHD-Leray-alpha equations which are similar to the MHD equations. We put forward the concept of weak and strong solutions for the new equations. Whether the 3-dimensional MHD equations have a unique weak solution is unknown, however, there is a unique weak solution for the 3-dimensional MHD-Leray-alpha equations. The global existence of strong solution and the Gevrey class regularity for the new equations are also obtained. Furthermore, we prove that the solutions of the MHD-Leray-alpha equations converge to the solution of the MHD equations in the weak sense as the parameter ε in the new equations converges to zero. |
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Keywords: | Navier-Stokes equations MHD equations MHD-Leray-alpha equations Weak solution Strong solution |
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