Local existence of compressible two-phase flows with phase transitions

開催日時
2015/05/15 金 15:30 - 17:30
場所
3号館251号室
講演者
清水 扇丈
講演者所属
京都大学大学院人間・環境学研究科
概要

We consider models for compressible two-phase flows with phase transitions. These are derived by first principles, i.e., balance of mass, momentum, and energy. As a first step, we analyze a simplified model, where the temperature is assumed to be constant. Performing a Hanzawa transform, the problem is transformed to a quasilinear parabolic two-phase problem with complicated transmission conditions on the interface in a fixed domain. Then the density can be considered as a function of the velocity and of the height function, applying the method of characteristics. We prove maximal Lp-regularity of a the corresponding linearized problem, and then by a fixed point argument in a suitable space, we obtain local existence of the isothermal model. This is a joint work with J. Pruess (Halle).