The aim of this short note is to explain important spectral phenomenon which can be observed for differential operators appearing in problems of magnetic hydrodynamics. This phenomenon are due to the nonperturbative behavior of the essential spectrum. It has been observed that the essential spectrum of a matrix differential operator on a finite interval can be different from the limit of the es...

In this note we continue the work in [SL], and give a full description of the essential spectrum for the linearized Euler operator L in dimension two. We prove that the essential spectrum of the operator is one solid vertical strip symmetric with respect to the imaginary axis. The width of the strip is determined by the maximal Lyapunov exponent Λ for the flow induced by the steady state. For c...