Boundary integral equations in quasisteady problems of capillary fluid mechanics. I: Application of the hydrodynamic potentials (Q804435)

The author has considered the motion of a viscous multiphase liquid occupying all the space under the action of surface tension. The flow is completely defined by the location of an interface for which the abstract Cauchy problem with nonlocal `normal velocity' operator is formulated by applying the quasisteady approximation. The fluid velocity is determined after solving the auxiliary problem for the Stokes system in a fixed domain and emphasis is made to construct the Fredholm boundary integral equations and to achieve the `normal velocity' operator using the specificity of the capillary forces. The used method of hydrodynamic potentials is practically important for numerical simulations; this method gives the opportunity to decrease the number of independent variables and to get rid of the infinite domains. As an example of this method, the stability problem of a spherical drop drift is also investigated by the author.