Traditional techniques for studying instabilities and waves in fluids and plasmas are based on the spectral analysis. In this talk various spectral problems occurring in hydrodynamics and magnetohydrodynamics are discussed. It is demonstrated how to apply modern methods of spectral theory for studying these problems. It is shown that a complicated interplay between the flow and the magnetic field produces rather unusual spectra. For a class of simple equilibria the corresponding spectral problems are described in detail. Various applications of spectral methods in controlled thermonuclear fusion, astrophysics, and geophysics are mentioned.
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