PIMS/AMI Seminar: On Singularity Formation of a Nonlinear Nonlocal System

We introduce a 2x2 nonlinear nonlocal system. On the one hand, it models possible blow-up mechanism in the 3D Euler equations; On the other hand, it can be seen as a further step in the recent progress in understanding the role of nonlocal operators in differential equations. We will present the following results: Local well-posedness for general initial data, global well-posedness for a class of special initial data, and finite-time singularity for another class of special initial data.