Global existence for a hyperbolic model of multiphase flows with few interfaces

Edda Dal Santo

Dottorato di ricerca in Matematica e Fisica (XXVIII ciclo)

In this thesis we consider a hyperbolic system of three conservation laws modeling the one-dimensional flow of a fluid that undergoes phase transitions. We address the issue of the global in time existence of weak entropic solutions to the initial-value problem for large BV data: such is a challenging problem in the field of hyperbolic conservation laws, that can be tackled only for very special systems. In particular, we focus on initial data consisting of either two or three different phases separated by interfaces. This translates into the modeling of a tube divided into either two or three regions where the fluid lies in a specific phase. In the case of two interfaces this possibly gives rise to a drop of liquid in a gaseous environment or a bubble of gas in a liquid one.