37 citations · 81 across the 20 of their papers we have counts for
20 papers
Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations
Xiaoming An, Lun Guo, Xiao Luo +1
We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric poten…
Three wave interaction solitons for an energy critical Schrödinger system
Luigi Forcella, Xiao Luo, Xiaolong Yang
We investigate standing waves for the energy critical Schrödinger system with three waves interaction arising as a model for the Raman amplification in a plasma. Several results ar…
Standing waves for two-component elliptic system with critical growth in : the attractive case
Lun Guo, Qi Li, Xiao Luo +1
In this paper, we consider the following two-component elliptic system with critical growth \begin{equation*} \begin{cases} -Δu+(V_1(x)+λ)u=μ_1u^{3}+βuv^{2}, \ \ x\in \mathbb{R}^4,…
Standing waves for a Schrödinger system with three waves interaction
Luigi Forcella, Xiao Luo, Tao Yang +1
We study standing waves for a system of nonlinear Schrödinger equations with three waves interaction arising as a model for the Raman amplification in a plasma. We consider the mas…
Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density
Xiao Luo, Yoshinobu Kuramashi
We apply the tensor renormalization group method to the (1+1)-dimensional SU(2) principal chiral model at finite chemical potential with the use of the Gauss-Legendre quadrature to…
Normalized solutions for Schrödinger system with quadratic and cubic interactions
Xiao Luo, Juncheng Wei, Xiaolong Yang +1
In this paper, we give a complete study on the existence and non-existence of normalized solutions for Schrödinger system with quadratic and cubic interactions. In the one dimensio…
Positive normalized solutions to nonlinear elliptic systems in with critical Sobolev exponent
Xiao Luo, Xiaolong Yang, Wenming Zou
In this paper, we consider the existence and asymptotic behavior on mass of the positive solutions to the following system: \begin{equation}\label{eqA0.1}\nonumber \begin{cases} -Δ…
Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent
Gongbao Li, Xiao Luo, Tao Yang
In this paper, we consider the existence and asymptotic properties of solutions to the following Kirchhoff equation \begin{equation}\label{1}\nonumber - \Bigl(a+b\int_{\R^3} {{{\le…
Multiplicity and asymptotics of standing waves for the energy critical half-wave
Xiao Luo, Tao Yang, Xiaolong Yang
In this paper, we consider the multiplicity and asymptotics of standing waves with prescribed mass to the energy critical half-wave \begin{equat…
Ground states for 3D dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses
Xiao Luo, Tao Yang
We consider ground states of three-dimensional dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses, which can be described equivalently by positiv…
Multiplicity, asymptotics and stability of standing waves for nonlinear Schrödinger equation with rotation
Xiao Luo, Tao Yang
In this article, we study the multiplicity, asymptotics and stability of standing waves with prescribed mass for nonlinear Schrödinger equation with rotation in the mass-supe…
Standing waves with prescribed mass for the Schrödinger equations with van der Waals type potentials
Daomin Cao, Huifang Jia, Xiao Luo
\begin{abstract} In this paper, we focus on the standing waves with prescribed mass for the Schrödinger equations with van der Waals type potentials, that is, two-body potentials w…
Nonuniqueness of weak solutions for the transport equation at critical space regularity
Alexey Cheskidov, Xiaoyutao Luo
We consider the linear transport equations driven by an incompressible flow in dimensions . For divergence-free vector fields , the celebrated DiPerna…
Anomalous dissipation, anomalous work, and energy balance for smooth solutions of the Navier-Stokes equations
Alexey Cheskidov, Xiaoyutao Luo
In this paper, we study the energy balance for a class of solutions of the Navier-Stokes equations with external forces in dimensions three and above. The solution and force are sm…
Normalized solutions for a fourth-order Schrödinger equation with positive second-order dispersion coefficient
Xiao Luo, Tao Yang
We are concerned with the existence and asymptotic properties of solutions to the following fourth-order Schrödinger equation \begin{equation}\label{1} Δ^{2}u+μΔu-λu={|u|}^{p-2}u,…
Stationary and discontinuous weak solutions of the Navier-Stokes equations
Alexey Cheskidov, Xiaoyutao Luo
We prove that there exists a nontrivial finite energy periodic stationary weak solution to the 3D Navier-Stokes equations (NSE). The construction relies on a convex integration sch…
Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions
Xiaoyutao Luo
Consider the unforced incompressible homogeneous Navier-Stokes equations on the -torus where is the space dimension. It is shown that there exist nontri…
Energy equality for the Navier-Stokes equations in weak-in-time Onsager spaces
Alexey Cheskidov, Xiaoyutao Luo
Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energ…
A Beale-Kato-Majda criterion with optimal frequency and temporal localization
Xiaoyutao Luo
We obtain a Beale-Kato-Majda-type criterion with optimal frequency and temporal localization for the 3D Navier-Stokes equations. Compared to previous results our condition only req…
On the possible time singularities for the 3D Navier-Stokes equations
Xiaoyutao Luo
We prove a local-in-time regularity criterion for the 3D Navier-Stokes equations. In particular, it follows from the criterion that the Hausdorff dimension of possible singular tim…