In this work, we study the Sobolev stability of shear flows near Couette in the 2D incompressible magnetohydrodynamics (MHD) equations with background magneticfield (alpha,0)(T)on TxR. More precisely, for sufficiently large alpha, we show that when the initial datum of the shear flow satisfies & Vert;U(y)-y & Vert;HN+6 1, and the initial perturbationsu in and b(in) satisfy & Vert;(u(in),b(in))& Vert;HN+1=0.
