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We study the long time asymptotic behavior of the inviscidmagnetohydrodynamic equations with magnetic dissipation near a combination ofCouette flow and a constant magnetic field. Here we show that there existnearby explicit global in time low frequency solutions, which we call waves.Moreover, the linearized problem around these waves exhibits resonances underhigh frequency perturbations, called echoes, which result in norm inflationGevrey regularity and infinite time blow-up in Sobolev regularity.

On Echoes in Magnetohydrodynamics with Magnetic Dissipation