The dynamics of a two-component fluid in the presence of capillary-forces. (English. Russian original) Zbl 0921.35134
Math. Notes 62, No. 2, 244-254 (1997); translation from Mat. Zametki 62, No. 2, 293-305 (1997).
Summary: We study the qualitative behavior as \(t\to\infty\) of the solution of the Cauchy problem for a system of equations describing the dynamics of a two-component viscous fluid. The model under consideration takes into account the mutual diffusion of the fluid components as well as their capillary interaction. We describe the \(\omega\)-limit set of trajectories of the dynamical system generated by the problem. It is proved that the stationary solution of the problem, a homogeneous stationary distribution of one of the components, is asymptotically stable. Any other stationary solution is not asymptotically stable and is even unstable if there are no close stationary solutions corresponding to a smaller energy level.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
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