Hopf bifurcation in viscous incompressible flow down an inclined plane (Q1773117)

The present paper is concerned with the two-dimensional motion of a viscous incompressible fluid flowing down an inclined plane under the effect of gravity. The motion takes place in a domain with a free boundary. The effect of the surface tension at the upper free surface is taken into account. The purpose of this paper is to provide the theorem which proves the existence of a time periodic solution bifurcating from the basic flow under certain assumptions. The problem is reduced to a fixed domain and the Lyapunov-Schmidt decomposition is applied.