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math-ph2025
Gagliardo-Nirenberg-Sobolev inequalities and ground states of Fermions in relativistic Hartree-Fock model
Yuan-da Wu, Xiaoyu Zeng, Yimin Zhang
This paper presents a rigorous mathematical analysis of the relativistic Hartree-Fock model for finite Fermi systems. We first establish an optimal Gagliardo-Nirenberg-Sobolev (GNS…
math.FA2025
Existence and Blow-up Profiles of Ground States in Second Order Multi-population Mean-field Games Systems
Fanze Kong, Juncheng Wei, Xiaoyu Zeng
In this paper, we utilize the variational structure to study the existence and asymptotic profiles of ground states in multi-population ergodic Mean-field Games systems subject to…
math.FA2025
Local Minimizers in Second Order Mean-field Games Systems with Choquard Coupling
Fanze Kong, Yonghui Tong, Xiaoyu Zeng
Mean-field Games systems (MFGs) serve as paradigms to describe the games among a huge number of players. In this paper, we consider the ergodic Mean-field Games systems in the boun…