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Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows

• In this paper we consider the equations of the unsteady viscous, incompressible, and heat conducting magnetohydrodynamic flows in a bounded three-dimensional domain with Lipschitz boundary. By an approximation scheme and a weak convergence method, the existence of a weak solution to the three-dimensional density dependent generalized incompressible magnetohydrodynamic equations with large data is obtained.
Mathematics Subject Classification: Primary: 76W05, 35D30.

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