$L_2$-theory for two incompressible fluids separated by a free interface

Irina V. Denisova, Vsevolod A. Solonnikov

Abstract


The paper is devoted to the problem of non-stationary motion of two viscous incompressible fluids separated by a free surface and contained in a bounded vessel. It is assumed that the fluids are subject to mass forces and capillary forces at the interface. We prove the stability of a rest state under the assumption that initial velocities are small, a free interface is close to a sphere at an initial instant of time, and mass forces decay as $t\to\infty$.

Keywords


Two-phase problem; viscous incompressible fluids; interface problem with suface tension; Navier-Stokes system; Sobolev-Slobodetskiĭ spaces

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References


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