PDE seminar: Stability of equilibria for incompressible two-phase flows with phase transitions

Date
2013-12-16 16:30 - 2013-12-16 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Senjo Shimizu (Shizuoka University)
 
A basic model for incompressible two-phase flows
with phase transitions consistent with thermodynamics
in a bounded domain in the case of constant
but non-equal densities of the phases is considered.
The local well-posedness of the problem is proved
by means of maximal $L_p$-regularity. We study
the stability of the equilibria of this system which
are zero velocities, constant temperature, constant
pressures in each phase, and the disperse phase
consists of a finite number of non-intersecting balls
of the same radius. The equilibria form a manifold.
We prove that an equilibrium is stable if and only if
the phases are connected, otherwise it is unstable.