Title
From the FPU Paradox to Kinetic Theory: Extended Lifespan for the Inhomogeneous Kinetic FPU Equation
Abstract
The Fermi–Pasta–Ulam (FPU) experiment revealed an unexpected lack of thermalization in weakly nonlinear oscillator chains, giving rise to the well-known FPU paradox.
Kinetic theory provides a natural framework to describe this phenomenon through effective equations governing phonon interactions.
In this talk, I will briefly review the kinetic description of the FPU–$\beta$ chain and recall a formal derivation framework for kinetic equations, developed by Germain et al., as background and motivation.
The main focus is the inhomogeneous kinetic FPU equation, which couples free transport in physical space with a degenerate collision operator in momentum space.
Using dispersive estimates for the linear transport semigroup, we show that small solutions near the vacuum admit an extended lifespan, improving the classical quadratic time scale to a quartic one
Kinetic theory provides a natural framework to describe this phenomenon through effective equations governing phonon interactions.
In this talk, I will briefly review the kinetic description of the FPU–$\beta$ chain and recall a formal derivation framework for kinetic equations, developed by Germain et al., as background and motivation.
The main focus is the inhomogeneous kinetic FPU equation, which couples free transport in physical space with a degenerate collision operator in momentum space.
Using dispersive estimates for the linear transport semigroup, we show that small solutions near the vacuum admit an extended lifespan, improving the classical quadratic time scale to a quartic one
Please note that the seminar will take place in person in room 140 of Huxley Building.