On the long time behaviour of the solution to the two-fluids incompressible Navier-Stokes equations
The paper deals with the long time behaviour of the solution to the system of the modified (two-fluids) incompressible Navier-Stokes equations and the surface tracking equation for the height function. The authors investigate the question: Do the equations reproduce the behaviour expected from experiments? They study the case with and without the surface tension at the interface both for the linearized model (around the steady-state of minimal energy) and the general nonlinear model. They obtain results that show a wide variety of behaviors (concerning a convergence of the velocity field and the interface to their stable positions). The results are formulated in 4 propositions (the linear and nonlinear case, the surface tension is or isn't considered). The article is a very interesting contribution to the two-fluid flow modelling.
scientific article; zbMATH DE number 1858766