68 citations · 577 across the 31 of their papers we have counts for
32 papers
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…
The second order Huang-Yang approximation to the Fermi thermodynamic pressure
Xuwen Chen, Jiahao Wu, Zhifei Zhang
We consider a dilute Fermi gas in the thermodynamic limit with interaction potential scattering length at temperature . We prove the 2nd order Huang-Yang appr…
-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…
The second order Huang-Yang formula to the 3D Fermi gas: the Gross-Pitaevskii regime
Xuwen Chen, Jiahao Wu, Zhifei Zhang
For a system of Fermions of spin , with its interaction potential of scattering length , the classical Huang-Yang formula states that the energy density is of th…
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…
The Second Order 2D Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime
Xuwen Chen, Jiahao Wu, Zhifei Zhang
We consider a system of bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normaliz…
The Derivation of the Boltzmann Equation from Quantum Many-body Dynamics
Xuwen Chen, Justin Holmer
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, ef…
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…
Well/ill-posedness bifurcation for the Boltzmann equation with constant collision kernel
Xuwen Chen, Justin Holmer
We consider the 3D Boltzmann equation with the constant collision kernel. We investigate the well/ill-posedness problem using the methods from nonlinear dispersive PDEs. We constru…
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…
Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space
Xuwen Chen, Justin Holmer
We consider the derivation of the defocusing cubic nonlinear Schrödinger equation (NLS) on from quantum -body dynamics. We reformat the hierarchy approach with…
The Unconditional Uniqueness for the Energy-critical Nonlinear Schrödinger Equation on
Xuwen Chen, Justin Holmer
We consider the cubic NLS which is energy-critical. We study the unconditional uniqueness of solution to the NLS via the cubic Gross-Pitaevskii hierarchy, an uncom…
The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics
Xuwen Chen, Justin Holmer
We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critic…
The Rigorous Derivation of the 2D Cubic Focusing NLS from Quantum Many-body Evolution
Xuwen Chen, Justin Holmer
We consider a 2D time-dependent quantum system of -bosons with harmonic external confining and \emph{attractive} interparticle interaction in the Gross-Pitaevskii scaling. We de…
Convergence to Equilibrium of a Body Moving in a Kinetic Sea
Xuwen Chen, Walter Strauss
We consider a continuum of particles that are acted upon by an external force and that collide with a rigid body. The body itself is subject to a constan…
On the Weak Coupling Limit of Quantum Many-body Dynamics and the Quantum Boltzmann Equation
Xuwen Chen, Yan Guo
The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam t…
Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy
Xuwen Chen, Justin Holmer
We consider the dynamics of bosons in three dimensions. We assume the pair interaction is given by . By studying an associated many-body wave operator,…
Focusing Quantum Many-body Dynamics II: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation from 3D
Xuwen Chen, Justin Holmer
We consider the focusing 3D quantum many-body dynamic which models a dilute bose gas strongly confined in two spatial directions. We assume that the microscopic pair interaction is…
On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
Xuwen Chen, Paul Smith
In this article we establish the unconditional uniqueness of solutions to an Infinite Radial Chern-Simons-Schrödinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarc…
Velocity Reversal Criterion of a Body Immersed in a Sea of Particles
Xuwen Chen, Walter Strauss
We consider a rigid body colliding with a continuum of particles. We assume that the body is moving at a velocity close to an equilibrium velocity V_{\infty} and that the particles…
Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
Xuwen Chen, Justin Holmer
We consider the dynamics of N bosons in one dimension. We assume that the pair interaction is attractive and given by N^{β-1}V(N^β\cdot) where \int V\leqslant 0. We develop new tec…