PDE seminar: Stability of equilibria for incompressible twophase flows with phase transitions
 Date

20131216 16:30 
20131216 17:30
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Senjo Shimizu (Shizuoka University)

 A basic model for incompressible twophase flows
with phase transitions consistent with thermodynamics
in a bounded domain in the case of constant
but nonequal densities of the phases is considered.
The local wellposedness 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 nonintersecting 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.