5 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…
-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 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 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…
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 t…