Abstract: We will discuss a recent joint work with Yu Deng (Chicago) and Xiao Ma (Michigan) which gave the rigorous derivation of the Boltzmann and fluid equations from Newton's laws. This executed the so-called "Hilbert’s Program", proposed in Hilbert's sixth problem from 1900, which asked for the derivation of fluid equations (like Euler’s and Navier-Stokes’) using Boltzmann’s kinetic theory as an intermediate step. The result follows parallel progress (by Deng and myself) in the wave setting, where colliding particles are replaced by interacting waves.

Bio: Dr. Hani is the Frederick W. and Lois B. Gehring Professor of Mathematics and his research is in the area of nonlinear partial differential equations (PDE). Particularly, I study equations modeling wave-type phenomena, which are often called nonlinear dispersive PDE.