4 papers · 1 filter
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 fo…
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…
Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation
Pierre Germain, Joonhyun La, Angeliki Menegaki
We study the nonlinear dynamics of the kinetic wave equation associated to the FPU problem and prove stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral…
Local Well-posedness for the Kinetic MMT Model
Pierre Germain, Joonhyun La, Katherine Zhiyuan Zhang
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is b…