# From Instability to Singularity Formation in Incompressible Fluids

## Location

The singularity formation problem is a central question in fluid dynamics, and it is still widely open for several fundamental models, including the 3d incompressible Euler equations. In this talk, I will first review the singularity formation problem, describing how particle transport poses the main challenge in constructing blow-up solutions — an effect known as “regularization by transport.” I will then outline a new mechanism that allows us to overcome regularization by transport, leveraging the instability seen in the classical Taylor-Couette experiment. Using this mechanism, we construct the first swirl-driven singularity for the incompressible Euler equations in R^3. This is joint work with Tarek Elgindi (Duke University).Abstract