MHD Equations in a Bounded Domain

We consider the MHD system in a bounded domain Ω ⊂ ℝ^N, N = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global in time, unique solutions to fractional approximations of the MHD system in the base space (L²(Ω ))^N × (L²(Ω ))^N. Solutions to MHD system are obtained next as a limits of that fractional approximations.