Stability of the Couette flow of ideal rigid-plastic bodies

The generalized Rayleigh stability problem is studied for the plane flows of ideal rigid-plastic bodies. The stationary scattering theory is used for the Couette flow to describe the structure of continuous and point spectra and to construct an expansion in eigenfunctions and in generalized eigenfunctions. Some integral estimates are proposed for the domain containing the spectrum of the problem to prove the stability of this flow.