3 papers
math.AP2026
Strichartz Estimates for the Liouville Equation on Euclidean Tori and Applications to Kakeya
Pierre Germain, Mickaël Latocca
We prove Strichartz estimates for the space-time density of solutions to the free Liouville equation on flat tori. In dimension one, we obtain the optimal range of estimates f…
math-ph2026
A review on the kinetic theory of oscillator chains
Pierre Germain, Joonhyun La, Angeliki Menegaki
We review the kinetic theory of one-dimensional nonlinear oscillator chains, of which the most famous example is the Fermi-Pasta-Ulam-Tsingou equation. We provide detailed, though…
math.AP2024
Entropy maximizers for kinetic wave equations set on tori
Miguel Escobedo, Pierre Germain, Joonhyun La +1
We consider the kinetic wave equation, or phonon Boltzmann equation, set on the torus (physical system set on the lattice). We describe entropy maximizers for fixed mass and energy…