My main field of research is analysis of partial differential equations. In particular, I study equations related to the theory of fluid mechanics and nonlinear dispersive waves. 

Many physical phenomena are governed by nonlinear partial differential equations, often constrained to bounded (possibly moving) domains. My goal is to understand some of those equations using  rigorous mathematics, and to prove new results that are physically significant. 

At the moment, I am working on free boundary hyperbolic systems and compressible fluid models. Those models describe the evolution of celestial bodies/water waves, and arise in the formulation of quantum fluids.