On an initial value problem concerning Taylor instability of incompressible fluids

By taking the effect of surface tension and viscosity into consideration, Bellman and Pennington [2] have generalized the original treatment of the problem of Taylor instability [1]. They claim, however, that a problem in which the motion starts from rest cannot be treated with their linearized formulation. In this paper, the initial value problem is treated and, although the algebra becomes more complicated, the linearized analysis suffices. In particular, the cut-off wave number as found in [2] is not modified.