arXiv subjects

Hangsheng Chen

Publications and source records attributed to Hangsheng Chen.

3 recordsLinked to original sources

arXiv2026

Revisiting Non-Rotating Star Models: Classical Existence and Uniqueness Theory and Scaling Relations

This paper presents a systematic study of the properties of non-rotating stellar models governed by the Euler-Poisson system under general equations of state, including the case of polytropic gaseous stars. We revisit and extend existence results by Auchmuty and Beals \cite{AB71}, adapt the uniqueness results from the quantum mechanical framework of Lieb and Yau \cite{LY87} to the classical Newtonian mechanical setting. The results are also synthesized in McCann \cite{McC06} but without proof. The second work we do is applying a scaling method to establish relations between solutions with different total masses. As the mass tends to zero, we analyze convergence properties of the density functions and identify precise rates for the contraction or extension of their supports.

math.AP↗

arXiv2026

Existence for Stable Rotating Star-Planet Systems

This paper investigates the existence and properties of stable, uniformly rotating star-planet systems, i.e. mass ratio is sufficiently small. It is modeled by the Euler-Poisson equations. Following the framework established by McCann for binary stars \cite{McC06}, we adopt a variational approach, and prove the existence of local energy minimizers with respect to the Wasserstein $L^\infty$ metric, under the assumed equation of state $P(ρ)=Kρ^γ$ and under the condition that the mass ratio $m$ is sufficiently small, corresponding to a star-planet system. Such minimizers correspond to solutions of the Euler-Poisson system. We consider two cases. For $γ> 2$, we not only prove existence but also show, via scaling arguments, that the radii (to be precise, the bounds of the supports of the minimizers) tend to zero. For $\frac{3}{2} < γ\leq 2$, we estimate an upper bound for the (potential) expansion rates of the radii, and it turns out that the existence result remains valid in this case as well. Finally, we provide estimates for the distances between different connected components of supports of minimizers and propose a conjecture regarding the number of connected components.

math.AP↗

arXiv2026

Gradient Existence and Energy Finiteness of Local Minimizers in the Wasserstein $L^\infty$ Topology for Binary-Star Systems

In this paper, we refine and complement McCann's results on binary-star systems \cite{McC06}, a compressible fluid model governed by the Euler-Poisson equations. We consider a general form of the equation of state that includes polytropic gaseous stars indexed by $γ$ as a special case. Beyond revisiting McCann's framework and conclusions -- where solutions to the Euler-Poisson equations are obtained as local energy minimizers via variational methods under the topology induced by the Wasserstein $L^\infty$ distance -- we focus on a detailed exploration of the properties of local energy minimizers in this topology, addressing three key aspects: (1) the feasibility of transitioning from the Euler-Lagrange equation to the Euler-Poisson equation by demonstrating gradient existence; (2) the existence of $L^\infty$ functions within neighborhoods in this topology; and (3) the finiteness of the energy of local minimizers in this topology, contrasted with the non-existence of finite-energy local minimizers and the existence of infinite-energy weak local minimizers in the topology inherited from topological vector spaces.

math.AP↗