Non-relativistic limit of fermion ground states for the relativistic Vlasov-Poisson system

In this paper, we study the non-relativistic limit for fermion ground states of the relativistic Vlasov-Poisson energy (rVP) under a mass constraint. Jang and Seok [Kinet. Relat. Models 15(4), 605–620, (2022)] constructed fermion ground states of (rVP), and Dolbeault et al. [Arch. Ration. Mech. Anal. 171(3), 301–327, (2004)] found fermion ground states of non-relativistic Vlasov-Poisson energy (VP). Applying a variational approach, we prove that as the speed of light c goes to the infinity, the fermion ground states of (rVP) converge strongly to the fermion ground states of (VP) with a same mass constraint.