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math.AP2026
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…
math.AP2025
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…
math.AP2025
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…