5 papers
Rigorous derivation of damped-driven wave turbulence theory
Ricardo Grande, Zaher Hani
We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schrödinger equation with an additive stochastic forcing and a viscous dissipation. The i…
Validity condition of normal form transformation for the -FPUT system
Boyang Wu, Miguel Onorato, Zaher Hani +1
In this work, we provide a validity condition for the normal form transformation to remove the non-resonant cubic terms in the -FPUT system. We show that for a wave field with…
Long time derivation of the Boltzmann equation from hard sphere dynamics
Yu Deng, Zaher Hani, Xiao Ma
We provide a rigorous derivation of Boltzmann's kinetic equation from the hard sphere system for rarefied gas, which is valid for arbitrarily long times, as long as the solution to…
Non-equilibrium steady state for a three-mode energy cascade model
Zaher Hani, Yao Li, Andrea Nahmod +1
Motivated by the central phenomenon of energy cascades in wave turbulence theory, we construct non-equilibrium statistical steady states (NESS), or invariant measures, for a simpli…
Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory
Yu Deng, Zaher Hani, Xiao Ma
In this paper, we rigorously derive the fundamental PDEs of fluid mechanics, such as the compressible Euler and incompressible Navier-Stokes-Fourier equations, starting from the ha…