Research Interests

My scientific work has focused on the analysis of certain fluid/flow structure (FSI) systems that include: (i) PDE models of vascular blood flow which take into account the multilayered nature of mammalian arterial structural walls; (ii) PDE models with incompressible and/or compressible multiflow components which are invoked in the design of aircraft, bridges and robotic systems. In my work, I have developed methodologies to obtain theoretical results such as wellposedness and stability properties of these FSI models. These methodologies partially entail dynamical systems theory, techniques from pseudodifferential analysis, spectral/resolvent analysis of linear operators, Galerkin methods, Lyapunov approach/energy estimates.

In addition, I have been interested and involved in numerical computation for those coupled multilayered PDE systems, structural acoustics and fluid-structure PDE systems which arise in biomedicine and aeroelasticity. To numerically simulate the solutions of the underlying partial differential equation (PDE), I am currently deriving mixed variational formulations, ultimately giving rise to mixed finite element method (FEM) which are amenable to a rigorous convergence analysis.

My research has partially been funded by National Science Foundation NSF-DMS-2206200, NSF-DMS-1907823, NSF-DMS-1616425.