2 citations · 5 across the 12 of their papers we have counts for
12 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…
Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system
Wendong Wang, Dongyi Wei, Zhifei Zhang
In this paper, we investigate critical mass threshold for the Patlak-Keller-Segel-Navier-Stokes system on the two-dimensional whole space and obtain global existence of strong solu…
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…
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…
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…
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…
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 hydrostatic approximation of the Navier-Stokes equations in a thin strip
M. Paicu, P. Zhang, Z. Zhang
In this paper, we first prove the global well-posedness of a scaled anisotropic Navier-Stokes system and the hydrostatic Navier-Stokes system in a 2-D striped domain with small ana…