I am Ken Furukawa. I have been studying mathematical analysis of partial differential equations related to the fluid dynamics and diffusion phenomena. For example, we studied mathematically rigorous justification of the derivation of the primitive equations by the Navier-Stokes equations. The primitive equations are a good model for fluid dynamics in thin domains and can be formally derived from a scaled Navier-Stokes equations. In mathematical studies, the global well-posedness for large data was established, which is a famous open problem in the case of the Navier-Stokes equations. We obtained a global well-posedness result to the scaled Navier-Stokes equations from the previous studies.

On the other hand, I am studying data assimilation of cellular automata with a particle filter method. I am also interested in the mathematical aspect of data assimilation. Data assimilation is very useful to predict the future state of dynamical systems. However, mathematically rigorous studies of data assimilation are under development. I will study data assimilation from a PDE point of view.