Landau damping can be defined as damping of a collective mode of oscillations in a collisionless plasma. Analogues of Landau damping has been observed in the sheared hydrodynamic flows and MHD waves. In this talk, I will report our recent results on the damping of the linearized 2-D Euler equations around the shear flow and the decay of Alfven waves in an inhomogeneous magnetic field.

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