57 citations · 125 across the 9 of their papers we have counts for
12 papers
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 r…
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…
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…
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 im…
Long time justification of wave turbulence theory
Yu Deng, Zaher Hani
In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multi…
Derivation of the wave kinetic equation: full range of scaling laws
Yu Deng, Zaher Hani
This paper completes the program started in arXiv:2104.11204 and arXiv:2110.04565 aiming at providing a full rigorous justification of the wave kinetic theory for the nonlinear Sch…
Rigorous justification of the wave kinetic theory
Yu Deng, Zaher Hani
The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain…
Propagation of chaos and the higher order statistics in the wave kinetic theory
Yu Deng, Zaher Hani
This manuscript continues and extends in various directions the result in arXiv:2104.11204, which gave a full derivation of the wave kinetic equation (WKE) from the nonlinear Schrö…
Full derivation of the wave kinetic equation
Yu Deng, Zaher Hani
We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that de…
On the derivation of the wave kinetic equation for NLS
Yu Deng, Zaher Hani
A fundamental question in wave turbulence theory is to understand how the "wave kinetic equation" (WKE) describes the long-time dynamics of its associated nonlinear dispersive equa…
A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds
Zaher Hani
We prove a bilinear estimate for a pair of oscillatory integral operators with different asymptotic parameters and phase functions sa…