21 citations · 45 across the 14 of their papers we have counts for
14 papers
Eigenvalue analysis of the Lax operator for the one-dimensional cubic nonlinear defocusing Schrödinger equation
Xian Liao, Michael Plum
We characterize the location and number of eigenvalues for the Lax operator associated to the one-dimensional cubic nonlinear defocusing Schrödinger equation. With the help of a ne…
Conserved energies for the one dimensional Gross-Pitaevskii equation: low regularity case
Herbert Koch, Xian Liao
We construct a family of conserved energies for the one dimensional Gross-Pitaevskii equation, but in the low regularity case (in \cite{KL} we have constructed conserved energies i…
On variable viscosity and enhanced dissipation
Xian Liao, Christian Zillinger
In this article we consider the 2D Navier-Stokes equations with variable viscosity depending on the vertical position. As our main result we establish linear enhanced dissipation n…
On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces
Zihui He, Xian Liao
We study the existence, uniqueness as well as regularity issues for the two-dimensional incompressible Boussinesq equations with temperature-dependent thermal and viscosity diffusi…
Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials
Xing Cheng, Chang-Yu Guo, Zihua Guo +2
In this paper, we consider the following three dimensional defocusing cubic nonlinear Schrödinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partia…
Nonlinear estimates for traveling wave solutions of reaction diffusion equations
Li-Chang Hung, Xian Liao
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of…
Conserved energies for the one dimensional Gross-Pitaevskii equation
Herbert Koch, Xian Liao
We prove the global-in-time well-posedness of the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced m…
Global regularity of three dimensional density patch for inhomogeneous incompressible viscous flow
Xian Liao, Yanlin Liu
The present work is devoted to proving that the boundary regularity of the three dimensional density patch persists by time evolution for inhomogeneous incompressible viscous flow,…
On the global regularity of 2-D density patch for inhomogeneous incompressible viscous flow
Xian Liao, Ping Zhang
Toward P.-L. Lions' open question in \cite{Lions96} concerning the propagation of regularity for density patch, we establish the global existence of solutions to the 2-D inhomogene…
A global existence result for a zero Mach number system
Xian Liao
This paper is to study global-in-time existence of weak solutions to zero Mach number system which derives from the full Navier-Stokes system, under a special relationship between…
Analysis of an inviscid zero-Mach number system in endpoint Besov spaces with finite-energy initial data
Francesco Fanelli, Xian Liao
The present paper is the continuation of work [14], devoted to the study of an inviscid zero-Mach number system in the framework of \emph{endpoint} Besov spaces of type $B^s_{\inft…
The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces
Francesco Fanelli, Xian Liao
The present paper is devoted to the study of a zero-Mach number system with heat conduction but no viscosity. We work in the framework of general non-homogeneous Besov spaces $B^s_…
The well-posedness issue in endpoint spaces for an inviscid low-Mach number limit system
Francesco Fanelli, Xian Liao
The present paper is devoted to the well-posedness issue for a low-Mach number limit system with heat conduction but no viscosity. We will work in the framework of general Besov sp…
On the well-posedness of the full low-Mach number limit system in general critical Besov spaces
Raphaël Danchin, Xian Liao
This work is devoted to the well-posedness issue for the low-Mach number limit system obtained from the full compressible Navier-Stokes system, in the whole space. In the case wher…