Global solvability of the problem on the motion of two fluids without surface tension |
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Authors: | I V Denisova |
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Institution: | (1) Institute of Mechanical Engineering Problems, Russian Academy of Sciences, St.Petersburg, Russia |
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Abstract: | 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 Hölder 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 small mass forces, we prove the existence of a unique smooth solution to the problem on an infinite time interval. Bibliography: 7 titles. |
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