Xuwen Chen

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20242026

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math.AP2026

Sharp $H_{x}^{s}$ 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 $H_{x}^{s}$ Sobolev space. Via a direct construction, we prove a strong-weak type ill-posedness…

math.AP2026

$l^{2}$ -decoupling and the unconditional uniqueness for the Boltzmann equation

Xuwen Chen, Shunlin Shen, Zhifei Zhang

We broaden the application of the $l^{2}$ -decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the $T^{d}$ setting. We estab…

math.AP2024

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 Hxs​ Ill-posedness of the Hard-sphere Boltzmann Equation

l2-decoupling and the unconditional uniqueness for the Boltzmann equation

Global derivation of the 1D Vlasov-Poisson equation from quantum many-body dynamics with screened Coulomb potential

Sharp $H_{x}^{s}$ Ill-posedness of the Hard-sphere Boltzmann Equation

$l^{2}$ -decoupling and the unconditional uniqueness for the Boltzmann equation