Well-posedness of the ferrimagnetic equations

In this paper, we show the existence of global weak solutions of the ferrimagnetic equations on compact Riemannian manifold using the penalty method. We also show the uniqueness of the solution and its well-posedness by the energy estimates method in lower dimensions. In particular, when the space dimension is one, we can prove that the problem is globally well-posed. © 2007 Elsevier Inc. All rights reserved.