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.

Intro
Turbulence, K'41
Intermittency
Mathematical considerations
Multiscale solutions
Construction of multiscale solns NSE
Time-dependent example: deterministic case
Time-dependent example, continued The solutions are smooth for all time. The energy is
Incompressible Fluid Pressure
Sufficient conditions for regularity, Navier-Stokes
Quantitative LSP
Criterion in terms of pressure
Ladyzhenskaya- Prodi-Serrin for Pressure
Structure function and regularity
Nearly selfsimilar example
Time dependent regions of interest
Multifractal scenario
Implementation
Representation formulas
Recap