##### Department of Mathematics,

University of California San Diego

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### Mathematics Colloquium

## Dr. Federico Pasqualotto

#### UC Berkeley

## From Instability to Singularity Formation in Incompressible Fluids

##### Abstract:

The singularity formation problem is a central question in fluid dynamics, and it is still widely open for fundamental models such as the 3d incompressible Euler equations and the Navier-Stokes equations. In this talk, I will first review the singularity formation problem, and I will describe 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, arising from the classical Taylor-Couette instability, allowing us to overcome regularization by transport in the 3d Euler equations, thereby constructing the first swirl-driven singularity in R^3. This is joint work with Tarek Elgindi (Duke University).

Host: Luca Spolaor

### December 5, 2023

### 4:00 PM

APM 6402 (Halkin Room)

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