Abstract
In this paper we discuss the MHD flow of a second grade fluid, in particular we prove the existence and uniqueness of a weak solution of a time-dependent grade two fluid model in a two-dimensional Lipschitz domain. We follow the methodology of Girault and Saadouni (Ref.[3]), i.e , we use a constructive method which can be adapted to the numerical analysis of finite-element schemes for solving this problem numerically.
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