Time-dependent example, continued The solutions are smooth for all time. The energy is
9
Incompressible Fluid Pressure
10
Sufficient conditions for regularity, Navier-Stokes
11
Quantitative LSP
12
Criterion in terms of pressure
13
Ladyzhenskaya- Prodi-Serrin for Pressure
14
Structure function and regularity
15
Nearly selfsimilar example
16
Time dependent regions of interest
17
Multifractal scenario
18
Implementation
19
Representation formulas
20
Recap
Description:
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.
Turbulence and Singularities in Fluid Flows - Mathematical Considerations