Turbulence and Singularities in Fluid Flows - Mathematical Considerations

Explore turbulence and singularities in fluid dynamics through this 55-minute lecture by Peter Constantin from Princeton University. Delve into topics such as K'41 intermittency, mathematical considerations of multiscale solutions, time-dependent examples in deterministic cases, and incompressible fluid pressure. Examine sufficient conditions for regularity in Navier-Stokes equations, quantitative LSP, and criteria in terms of pressure. Investigate the Ladyzhenskaya-Prodi-Serrin theorem for pressure, structure function and regularity, and nearly self-similar examples. Gain insights into time-dependent regions of interest, multifractal scenarios, implementation techniques, and representation formulas. This talk, part of the Workshop on Geometry and Analysis of Fluid Flows with a Special Tribute to David Ebin, offers a comprehensive overview of advanced concepts in fluid dynamics and mathematical analysis.