29 citations · 142 across the 32 of their papers we have counts for
8 papers · 1 filter
Dimension-dependent symmetry breaking in a diffusive nonlocal interaction model
Dohyun Kim, Hansol Park, Woojoo Shim
We study the equilibrium structure and long-time behavior of a nonlinear Fokker--Planck equation with diffusion and nonlocal interactions generated by squared simplex volumes. For…
Finite-dimensional reduction of a Wasserstein gradient flow and sharp decay rates
Dohyun Kim, Hansol Park, Woojoo Shim
We study the Wasserstein gradient flow generated by a family of extended generalized variance functionals, defined as the expected squared -dimensional volume of a simplex, whic…
Aggregation-diffusion energies on Cartan-Hadamard manifolds of unbounded curvature
Razvan C. Fetecau, Hansol Park
We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with sectional curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic aggr…
Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature
Razvan C. Fetecau, Hansol Park
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models s…
Equilibria and energy minimizers for an interaction model on the hyperbolic space
Razvan C. Fetecau, Hansol Park
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical po…
Emergent behaviors of the kinetic Lohe Hermitian sphere model
Junhyeok Byeon, Seung-Yeal Ha, Gyuyoung Hwang +1
We study a global well-posedness of measure-valued solutions to the kinetic Lohe Hermitian sphere(LHS) model derived from the Lohe tensor(LT) model on the set of rank-1 complex ten…
The Watanabe-Strogatz transform and constant of motion functionals for kinetic vector models
Hansol Park
We present a kinetic version of the Watanabe-Strogatz(WS) transform for vector models in this paper. From the generalized WS-transform, we obtain the cross-ratio type constant of m…
An intrinsic aggregation model on the special orthogonal group : well-posedness and collective behaviours
Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park
We investigate an aggregation model with intrinsic interactions on the special orthogonal group . We consider a smooth interaction potential that depends on the squared intr…