On well-posedness of the Cauchy problem for MHD system in Besov spaces

This paper studies the global well-posedness of solutions to the Cauchy problem of incompressible magneto-hydrodynamics system for large initial data in homogeneous Besov space Ḃ 2 p −1 p,r (R) for 2 < p < ∞ and 1 ≤ r < ∞. In the case of spatial dimension n ≥ 3 we establish the global well-posedness of solution for small data and the local one for large data in Besov space Ḃ n p −1 p,r (R), 1 ≤ p < ∞ and 1 ≤ r ≤ ∞. Moreover, we also prove the weak-strong uniqueness of solutions with data in Ḃ n p −1 p,r (R) ∩ L(R) for n 2p + 2 r > 1. AMS Subject Classification 2000: 76W05, 74H20, 74H25.