Global existence of weak solution to a two-fluid model with large initial data

We shall talk about the global existence of weak solutions of Dirichlet problem for a one-velocity viscous two-fluid model. By relying on weak compactness tools we obtain existence results within the class of weak solutions in one dimension and in high dimensions respectively. An essential novel aspect of the analysis, compared with previous works, is that the solution space is large enough to allow for transition to single-phase flow without any constraints in one dimension. In multi-dimensions, similar result can be obtained subject to some constraints for the adiabatic index. These works are joint with Steinar Evje (UiS, Norway), Alexis Vasseur (UT, Austin), Cheng Yu (UT, Austin), Changjiang Zhu (SCUT, China).