Asymptotic Stability of Couette Flow in a Strong Uniform Magnetic Field for the Euler-MHD System

In this paper, we prove the asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system, when the perturbations are in Gevrey-1s, (12<s≦1) and of size smaller than the resistivity coefficient μ. More precisely, we prove that the μ^-13-amplification of the perturbed vorticity, namely, the size of the vorticity grows from ‖ω_in‖Gλ₀≲μ to ‖ω_∞‖Gλ_′≲μ²³; the polynomial decay of the perturbed current density, namely, j≠L₂≲c₀⟨t⟩²minμ^-13,⟨t⟩; and the damping for the perturbed velocity and magnetic field, namely, (Formula presented.) We also confirm that the strong uniform magnetic field stabilizes the Euler-MHD system near Couette flow.