The Navier-Stokes equations, initially formulated in the early 19th century, have since become the cornerstone of fluid mechanics, subsequently extending their relevance to fluid geophysics. The existence and regularity of their solutions pose a significant challenge within a substantial domain of geophysics.

Over the years, a series of partial results have been obtained, particularly in the pursuit of proving one of the four statements proposed by Charles L. Fefferman for the Millennium Clay Prize. A definitive proof of the third statement regarding the breakdown of the Navier-Stokes equations was unveiled by OpenAI on September 8th, utilising extensive IA resources. This revelation has sparked a substantial debate, encompassing various aspects such as the physical significance of the blowing-up singularity, the utilisation of intensive AI resources in disruptive research, and the connections with concepts like intermittency, cascades, multifractals and enstrophy catastrophe. It may also inspire new approaches to resolve fundamental questions of geosciences.

This PICO session seeks to provide the geophysical community with an opportunity to contribute to this ongoing discourse.