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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.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…