11 citations · 25 across the 15 of their papers we have counts for
16 papers
Sharp Strichartz estimates on quadratic irrational tori
Rui Liang, Shunlin Shen, Yuzhao Wang
We prove sharp Strichartz estimates for two-dimensional periodic Schrödinger flows with integral diagonal symbols where $a,b \in \mathbb Z \setminus \{0\}…
Unconditional Uniqueness for the Energy-critical and Energy-supercritical Quadratic NLS
Shunlin Shen
We study the quadratic nonlinear Schrödinger equation in energy-critical and energy-supercritical regimes and establish unconditional uniqueness at critical regularity on both $\ma…
Norm inflation for the cubic hyperbolic NLS on
Shunlin Shen, Yuzhao Wang
We prove norm inflation for the cubic hyperbolic nonlinear Schrödinger equation in for every . The scaling-critical point i…
Sharp Ill-posedness of the Hard-sphere Boltzmann Equation
Xuwen Chen, Yan Guo, Shunlin Shen +1
We investigate the ill-posedness mechanism of the hard-sphere Boltzmann equation in Sobolev space. Via a direct construction, we prove a strong-weak type ill-posedness…
Asymptotic stability threshold of the 2-D monotone shear flow with no-slip boundary condition
Zhen Li, Shunlin Shen, Zhifei Zhang
In this paper, we investigate the asymptotic stability threshold problem for the 2-D Navier-Stokes equations in a finite channel with no-slip boundary conditions, around monotone s…
Asymptotic stability of the symmetric flow via inviscid damping and enhanced dissipation
Qi Chen, Hao Li, Shunlin Shen +1
In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the n…
Global stability of the inhomogeneous sheared Boltzmann equation in torus
Renjun Duan, Shuangqian Liu, Shunlin Shen
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging…
-decoupling and the unconditional uniqueness for the Boltzmann equation
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We broaden the application of the -decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the setting. We estab…
Derivation of the compressible Euler equations from the dynamics of interacting Bose gas in the hard-core limit regime
Jacky Chong, Shunlin Shen, Zhifei Zhang
We investigate the dynamics of short-range interacting Bose gases with varying degrees of diluteness and interaction strength. By applying a combined mean-field and semiclassical s…
Global derivation of the 1D Vlasov-Poisson equation from quantum many-body dynamics with screened Coulomb potential
Xuwen Chen, Shunlin Shen, Ping Zhang +1
We study the 1D quantum many-body dynamics with a screened Coulomb potential in the mean-field setting. Combining the quantum mean-field, semiclassical, and Debye length limits, we…
Sharp Global Well-posedness and Scattering of the Boltzmann Equation
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the 3D Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff. We prove sharp global well-posedness with initial data small in the sca…
Well/Ill-posedness of the Boltzmann Equation with Soft Potential
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-pos…
On the mean-field and semiclassical limit from quantum -body dynamics
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive -type potential and a Coulomb potential, which leads to a macr…
The derivation of the compressible Euler equation from quantum many-body dynamics
Xuwen Chen, Shunlin Shen, Jiahao Wu +1
We study the three dimensional many-particle quantum dynamics in mean-field setting. We forge together the hierarchy method and the modulated energy method. We prove rigorously tha…
The unconditional uniqueness for the energy-supercritical NLS
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the cubic and quintic nonlinear Schrödinger equations (NLS) under the and energy-supercritical setting. Via a newly developed unified…
The rigorous derivation of the focusing cubic NLS from 3D
Shunlin Shen
We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary co…