Jahed Abedi , Dipanjan Dey , Puskar Mondal , Alejandro Torres-Orjuela

Puskar Mondal

Thursday, September 17, 2026 2:30 PM - 3:30 PM

A3-2-301

Zoom 928 682 9093 (BIMSA)

A recent OpenAI work proposes a construction of a finite-time singular solution to the three-dimensional Navier-Stokes equations, supported by an extensive sequence of analytic estimates. In this talk, I will first explain the main structural ideas behind the construction, with an emphasis on the underlying mechanism rather than the full technical implementation. I will then discuss the extent to which such a solution should be regarded as dynamically robust or physically realizable. This leads naturally to the question of liberalized stability (as a first step). I will describe a framework for perturbing both the concentrating background flow and the auxiliary pulse structure responsible for the delicate cancellations in the construction, and discuss whether these cancellations persist under small perturbations. The aim is to identify possible growing modes or instability mechanisms associated with the singular dynamics. The stability analysis presented in the latter portion of the talk is part of ongoing work with Nikos Athanasiou and Prof. Shing-Tung Yau.

Puskar Mondal is currently an assistant professor in BIMSA. He's been a fellow and lecturer at Harvard CMSA of Mathematics (his mentor is Prof. Shing-Tung Yau), and was a Ph.D. student at Yale University, under the supervision of Prof. Vincent Moncrief.