Fluid Equations, A Paradigm for Complexity: Regularity vs Blow-up, Deterministic vs Stochastic (23w5040)

Fluids are ubiquitous in the nature, but equations of fluid mechanics are among the most difficult PDEs to analyze. The question of global regularity v.s. finite time blow-up remains open for many fundamental fluid equations, and there are also many other interesting open questions on other aspects of properties. Recently, the study of fluid equations has witnessed multiple breakthrough results, such as non-existence of type-one singularity, rigorous proofs for small scale formation and finite-time blow-up for various equations, non-uniqueness of weak solutions to the Euler and Navier-Stokes equation via convex integration, as well as the non-uniqueness of the law of the 3D stochastic Navier-Stokes equations. With these exciting developments in the last decade, this workshop is a timely event to capitalize on this momentum.

In this workshop, we aim to bring together leading experts and junior researchers covering complementary areas in fluid equations to share new ideas, discuss emerging problems, and identify promising research directions for the future. When inviting participants to the workshop, preferences will be given to junior researchers and researchers from underrepresented groups.