My research interests are in the analysis of nonlinear partial differential equations (PDEs), especially conservation laws which change type from hyperbolic to elliptic. My main interest is studying the well-posedness of and dynamics of the solutions to multidimensional problems, especially those problems related to compressible gases or fluids which are modelled by the full Euler system and various simplified systems related to the full Euler system. While well-posedness for conservation laws in one space dimension is relatively well-understood, the question of well-posedness for conservation laws in more than one space dimension is still widely open. Since the full Euler system and related systems model physical reality and they have been thoroughly tested by numerical simulations and experiments, one might expect well-posedness of these systems with suitable physical data. Studying prototype cases with these systems will not only provide insights on the underlying physical and engineering problems but also on the general theory of well-posedness for conservation laws in more than one space dimension.