I am interested in developing mathematical models which provide an averaged or coarse-grained description of complex problems. I also investigate numerical methods for interface problems. One area in which these approaches are useful is fluid mechanics; in particular two-fluid flow (air-water). This area is interesting for two reasons:
It is important for various engineering applications.
It provides very interesting and rich problems in applied mathematics.
For the most part the models I develop or study are formulated as partial differential equations. I am interested in the derivation of these equations, their asymptotic behavior, and finding solutions using numerical methods. A wide variety of mathematical tools are useful in solving these problems. We use tools from dynamical systems, harmonic analysis, real analysis, functional analysis, classical mechanics, kinetic theory, asymptotic analysis and numerical analysis.
