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James Glimm

AMS Colloquium: Non-Smooth Solutions of the Navier-Stokes Equation and Related Implications in Physics

Speaker: James (Jim) Glimm

Wednesday, October 22, 2025

12:30 pm

Math 1-122A (AMS Seminar Room)

Abstract: I will present a proposed solution for the well publicized fluids Millennium Prize problem with non-smooth solutions for all "turbulent" initial data. The talk will emphasize conceptual ideas, and I will try to make the ideas understandable, minimizing analytical details. I will outline the proof, which relies on some spherical and solid harmonics, but will try to make the ideas accessible to a diverse mathematical audience. Unavoidable details arise in the definition of a weak solution, a strong solution and a Leray-Hopf solution. I will also discuss extensions to Yang-Mills quantum fields and to quantum general relativity. Remarkably, the conceptual ideas require little change to address the Yang-Mills Millennium Prize problem and the construction of quantum general relativity, with a bonus: zero dark energy.

About the speaker: James (Jim) Glimm is a Distinguished Professor in Applied Mathematics and Statistics, where he served as Chair for over 20 years. He is a member of the National Academy of Science and won the National Medal of Science "For his original approaches and creative contribution to an array of disciplines in mathematical analysis and mathematical physics". He received the Leroy P. Steele Prize for his contributions to solving hyperbolic systems of partial differential equations. He has been both an Invited Speaker and a Plenary Speaker at the ICM. He is a former President of and current Fellow of the American Mathematical Society.