12 citations · 22 across the 13 of their papers we have counts for
6 papers · 1 filter
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…
Almost sharp wave kinetic theory of multidimensional KdV type equations with
Xiao Ma
In this work, we study the random series expansion of a multidimensional KdV type equation with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random i…
Linear Stability of the 2D Irrotational Circulation Flow around An Elliptical Cylinder
Xiao Ma
In this article we prove a linear inviscid damping result with optimal decay rates of the 2D irrotational circulation flow around an elliptical cylinder. In our result, all compone…
Cancellations of Resonances and Long Time Dynamics of Cubic Schrödinger Equation on
Kexin Jin, Xiao Ma
We prove a vanishing property of the normal form transformation of the 1D cubic nonlinear Schrödinger (NLS) equation with periodic boundary conditions on . We apply this pro…
Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case
Ze Li, Xiao Ma, Lifeng Zhao
In this paper, we prove that the small energy harmonic maps from to are asymptotically stable under the wave map equation in the subcritical perturbation clas…