Large Norm Inflation of the Current in the Viscous, Nonresistive Magnetohydrodynamics Equations

We consider the ideally conducting, viscous magnetohydrodynamics equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow and a constant magnetic field in a periodic infinite channel. In contrast to the Navier–Stokes equations this system is shown to exhibit algebraic instability and large norm inflation of the magnetic current on nonperturbative time scales.