Applied Mathematics Colloquium: Dr Huy Quang Nguyen

Title: Free-boundary problems in fluid dynamics 

Abstract: Free-boundary problems arise in many applications of fluid dynamics in science and engineering. These problems involve fluid flows in domains whose entire boundary or a part of it is dynamic and evolves according to couplings with the fluid fields. Free-boundary problems are challenging due to their notorious complexity, severe nonlocality and implicit nonlinearity. In the first part of the talk, I will discuss recent results on the well-posedness theory and the existence of global-in-time solutions and self-similar solutions for the Muskat problem for flows in porous media. In the second part, I will discuss recent results on the modulational instability of periodic travelling waves (Stokes waves) for the classic water wave problem.