On the Spectrum of the Orr-Sommerfeld Equation on the semiaxis
  The Orr-Sommerfeld equation is a spectral problem which is known to play an important role in hydrodynamic stability. For an appropriate operator theoretical realization of the equation, we will determine the essential spectrum, and calculate an enclosure of the set of all eigenvalues by elementary analytical means. 
Jan-R. Lahmann, Michael Plum