On the stability of steady surface-tension driven flows (Q1590404)

The authors study the stability of similarity solutions to a third-order nonlinear differential equation having a special form, derived from the symmetric reduction of similarity transformations from the Navier-Stokes equation for the planar flow. The solutions to this differential equation can be divided into three types: I ,II , III , depending on the coefficients of the equation. For stability analysis of the solutions, the authors impose an associated eigenvalue problem. The behavior of the eigenvalues of the solutions are analyzed by means of a small perturbation. The mathematical results are verified numerically.