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In this paper, we study the long-time behavior of the solution for thelinearized ideal MHD around sheared velocity and magnetic field under Sternstability condition. We prove that the velocity and magnetic field willconverge to sheared velocity and magnetic field as time approaches infinity.Moreover a new depletion phenomenon is proved: the horizontal velocity andmagnetic field at the critical points will decay to 0 as time approachesinfinity.

Linear damping and depletion in flowing plasma with strong sheared magnetic fields