6 citations · 12 across the 7 of their papers we have counts for
7 papers
On the spectra of the gravity water waves linearized at monotone shear flows
Xiao Liu, Chongchun Zeng
We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow , , where the wave numbers of the horiz…
Instability and spectrum of the linearized two-phase fluids interface problem at shear flows
Xiao Liu
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and…
Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping
Xiao Liu, Chongchun Zeng
This paper is concerned with the eigenvalues and linear inviscid damping of the 2D capillary gravity water waves of finite depth linearized at a monotone shear flow…
Focusing Singularity in a Derivative Nonlinear Schrödinger Equation
Xiao Liu, Gideon Simpson, Catherine Sulem
We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, . In the -supercritical regime, , our simulati…
Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation
Xiao Liu, Gideon Simpson, Catherine Sulem
We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability…
Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence
Xiao Liu, Yaron Oz
We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions…