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We consider mixtures of compressible viscous fluids consisting of two miscible species. In contrast to the theory of non-homogeneous incompressible fluids where one has only one velocity field, here we have two densities and two velocity fields assigned to each species of the fluid. We obtain global classical solutions for quasi-stationary Stokes-like system with interaction term.

On the attenuation of waves propagating in fluid mixtures.

Molotkov, L.A. (2005)

Zapiski Nauchnykh Seminarov POMI

On the extremals of a subsidiary capillary problem.

Paul Concus, Robert Finn (1984)

Journal für die reine und angewandte Mathematik

On the inequalities associated with a model of Graffi for the motion of a mixture of two viscous, incompressible fluids

Giovanni Prouse, Anna Zaretti (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We demonstrate a theorem of existence and uniqueness on a large scale of the solution of a system of differential disequations associated to a Graffi model relative to the motion of two incompressible viscous fluids.

On the Stefan problem: the variational approach and some applications

Alain Damlamian (1985)

Banach Center Publications

On unsteady two-phase fluid flow due to eccentric rotation of a disk.

Ghosh, A. K., Paul, S., Debnath, L. (2003)

International Journal of Mathematics and Mathematical Sciences

Properties of the Gibbs potential and the equilibrium of a liquid with its vapor

Antonio Romano (1983)

Rendiconti del Seminario Matematico della Università di Padova

Quando è possibile formare bolle in un fluido, e quando no

Epifanio G. Virga (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Bubbles are formed in a fluid by inflating a liquid film with a gas in which the pressure $\hat{\pi}(\nu)$ is a strictly decreasing function of the specific volume, unbounded as $\nu\rightarrow 0^{+}$ . We show that, if $\hat{\pi}(\nu)$ grows as fast or faster than $\nu^{-2/3}$ as $\nu\rightarrow 0^{+}$ , then there is at least one stable equilibrium configuration of any such bubble, no matter how much gas has been used to inflate it. On the other hand, if $\hat{\pi}(\nu)$ grows as slowly or slower than $\nu^{-1/3}$ as $\nu\rightarrow 0^{+}$ , then any such bubble has no equilibrium configuration, when the amount of gas within...