Behavior at infinity of solutions of operator differential equations connected with certain problems of hydrodynamics

In the present communication the stability and stabilization criteria at infinity are established for solutions of three-term differential equation whose coefficients are comutative self-adjoint operators (c.s.o.) on a Hilbert space. Such equations simulate certain physical processes (see, for example, [1-3]). The criteria are given in the terms of allocation of spectrums of the coefficients. It enables in concrete problems arising in hydrodynamics to determine the limits within which the equation parameters must change for the considered process to be stable.