Well-posedness for the incompressible magneto-hydrodynamic system

This paper is concerned with well-posedness of the incompressible magneto-hydrodynamics (MHD) system. In particular, we prove the existence of a global mild solution in BMO-1 for small data which is also unique in the space C([0, (infinity)); BMO-1). We also establish the existence of a local mild solution in bmo-1 for small data and its uniqueness in C([0, T); bmo-1). In establishing our results an important role is played by the continuity of the bilinear form which was proved previously by Kock and Tataru. In this paper, we give a new proof of this result by using the weighted Lp-boundedness of the maximal function.