The strong Onsager conjecture: A glimpse of turbulence

In the study of fluid dynamics, turbulence poses a significant challenge in predicting fluid behavior, and it remains a mystery for mathematicians and physicists alike. Recently, there has been some exciting progress in our understanding of ideal turbulence: starting from Onsager’s theorem to the resolution of strong Onsager's conjecture in $L^3$-framework. These developments have been accompanied by mathematical advances in Nash’s iteration. In this talk, I will provide an overview of turbulence and discuss these results.