6 papers
Global Finite-Energy Weak Solutions and Sharp Entropy Decay for a Poisson-Nernst-Planck System with Interspecies Drag and Steric Effects
Baoli Hao, Fanze Kong, Kei Fong Lam +1
We derive and analyze a binary Poisson-Nernst-Planck system with steric interactions and interspecies drag through the energetic variational approach. The steric effects are incorp…
Global Well-posedness of the 2D Stochastic Self-consistent Keller-Segel-Navier-Stokes System with Subcritical Cellular Mass
Fanze Kong, Chen-Chih Lai, Krutika Tawri
We consider a stochastic Keller-Segel-Navier-Stokes system in describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by…
Mountain-Pass Solutions for Second-Order Ergodic Mean-Field Game Systems
Fanze Kong, Yonghui Tong, Xiaoyu Zeng
We study the existence of mountain-pass solutions to a potential-free mean-field game system in the whole space under the mass-supercritical regime, assuming an aggre…
Stability and slow dynamics of an interior spiky pattern in a one-dimensional spatial Solow model with capital-induced labor migration
Fanze Kong, Jiayi Sun, Shuangquan Xie
One of the most significant findings in the study of spatial Solow-Swan models is the emergence of economic agglomeration, in which economic activities concentrate in specific regi…
Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
Fanze Kong, Chen-Chih Lai, Yubin Lu
Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift…
Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
Fanze Kong, Chen-Chih Lai, Yubin Lu
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws wit…