## 偏微分方程式セミナー: Stability of equilibria for incompressible two-phase flows with phase transitions

2013年 　 12月 16日 16時 30分 ～ 2013年 　 12月 16日 17時 30分

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.