  The present research is devoted to the problem of stability of the fluid flow
moving in a channel with flexible walls and interacting with the walls, which
are subject to traveling waves. Experimental data shows that the energy of the
flowing fluid can be transferred and consumed by the structure (the walls),
which induces "traveling wave flutter." The problem of stability of
fluid-structure interaction splits into two parts: (i) stability of fluid flow
in the channel with harmonically moving walls and (ii) stability of solid
structure participating in the energy exchange with the flow. Stability of
fluid flow is the main focus of the research. It is shown that using the mass
conservation and the incompressibility condition one can obtain the initial
boundary value problem for the stream function. The boundary conditions reflect
the facts that (i) for the axisymmetrical flow, there is no movement in the
vertical direction along the axis of symmetry, and (ii) there is no relative
movement between the near boundary flow and the structure ("no-slip"
condition). The closed form solution is derived and represented in the form of
an infinite functional series.
