GLOBAL SOLVABILITY OF THE PROBLEM ON THE MOTION OF TWO FLUIDS WITHOUT SURFACE TENSION

摘要

Unsteady motion of viscous incompressible fluids is considered in a bounded domain. The. liquids are separated by an unknown interface on which the surface tension is neglected. This motion is governed by an interface problem for the Navier-Stokes system. First, a local existence theorem is established for the problem, in Hoelder classes of functions. The proof is based on the solvability of a model problem for the Stokes system, with a plane interface, which was obtained earlier. Next, for a small initial velocity vector field and, sm,all m,ass forces, we. prove the existence of a unique smooth solution to the problem on an infinite time interval.