The analysis of multiphase flow models, such as models governing fluid-particle interaction and evolution of cells, is relevant to several practical applications in engineering and in physical and biomedical sciences. This project focuses on issues of stability, uniqueness and regularity, and numerical approximations for nonlinear models. In particular, the projects include analyzing systems involving moving domains or free boundaries and systems with stochastic forcing. The project includes undergraduates, graduate students, and post-doctoral associates in the research.
This research project focuses on the modeling and mathematical analysis of nonlinear systems arising in physical and biological science and addresses themes in two interconnected directions: (a) hydrodynamic models within moving domains and free boundary problems, and (b) random perturbations of models of compressible fluids and multiphase flows. The mathematical analysis of these nonlinear models requires innovative ideas for the construction of suitable schemes for the approximation of their governing systems, as well as the development of new analytical techniques for the proof of well-posedness and convergence results in light of special features of the models that arise in applications. The goal of the project is the development of a variational framework able to treat a large class of multi-phase flows both analytically and computationally. The nonlinear systems under investigation include models of compressible fluids governed by the Navier-Stokes and Euler systems, Euler-kinetic fluid models, mixed-type hyperbolic-elliptic systems within fixed or moving domains, and free-boundary models.
