- Series
- PDE Seminar
- Time
- Thursday, March 31, 2022 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 114
- Speaker
- Zaher Hani – University of Michigan
- Organizer
- Chongchun Zeng
Please Note: Meeting also available online: https://gatech.zoom.us/j/92742811112
Wave turbulence is the theory of nonequilibrium statistical mechanics for wave systems. Initially formulated in pioneering works of Peierls, Hasselman, and Zakharov early in the past century, wave turbulence is widely used across several areas of physics to describe the statistical behavior of various interacting wave systems. We shall be interested in the mathematical foundation of this theory, which for the longest time had not been established.
The central objects in this theory are: the "wave kinetic equation" (WKE), which stands as the wave analog of Boltzmann’s kinetic equation describing interacting particle systems, and the "propagation of chaos” hypothesis, which is a fundamental postulate in the field that lacks mathematical justification. Mathematically, the aim is to provide a rigorous justification and derivation of those two central objects; This is Hilbert’s Sixth Problem for waves. The problem attracted considerable interest in the mathematical community over the past decade or so. This culminated in recent joint works with Yu Deng (University of Southern California), which provided the first rigorous derivation of the wave kinetic equation, and justified the propagation of chaos hypothesis in the same setting.
Meeting also available online: https://gatech.zoom.us/j/92742811112