Yu Deng: The Hilbert Sixth Problem: Particles and Waves (December 6, 2024)
Автор: Simons Foundation
Загружено: 2025-04-08
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Описание:
A major component of the Hilbert sixth problem concerns deriving macroscopic equations of motion, and the associated kinetic equations, from microscopic first principles. In the classical setting of Boltzmann’s kinetic theory, this corresponds to deriving the Boltzmann equation from particle systems governed by Newtonian dynamics. In the theory of wave turbulence, it corresponds to deriving the wave kinetic equation from nonlinear dispersive equations.
In this talk, I will present recent joint work with Zaher Hani and Xiao Ma, where we examine the hard sphere model in the particle setting and the cubic nonlinear Schrödinger equation in the wave setting. In both cases, we derive the corresponding kinetic equation for as long as the solution to this kinetic equation exists. This represents a crucial step toward resolving the Hilbert sixth problem.
For more information go here: https://www.simonsfoundation.org/even...
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