6 citations · 23 across the 12 of their papers we have counts for
15 papers
Existence of weak solutions for fast diffusion equation with a divergence type of drift term
Sukjung Hwang, Kyungkeun Kang, Hwa Kil Kim
We construct non-negative weak solutions of fast diffusion equations with a divergence type of drift term satisfying the -energy inequality and speed estimate in Wasserstein s…
Existence of weak solutions for nonlinear drift-diffusion equations with measure data
Sukjung Hwang, Kyungkeun Kang, Hwa Kil Kim +1
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with measure data. We establish the existence of nonnegative weak soluti…
Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme
Kyungkeun Kang, Hwa Kil Kim, Geuntaek Seo
We consider a parabolic-elliptic type of Keller-Segel equations with generalized diffusion and logistic source under homogeneous Neumann-Neumann boundary conditions. We construct b…
Existence of weak solutions for Porous medium equation with a divergence type of drift term
Sukjung Hwang, Kyungkeun Kang, Haw Kil Kim
We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of -weak solutions (satisfying energy estimates or even furt…
Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow
Young-Pil Choi, Kyungkeun Kang, Hwa Kil Kim +1
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of…
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials
Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim +1
In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive-attractive potentials of power-law type in one dimension. We prove that sum of…
Well-posedness of strong solutions for the Vlasov equation coupled to non-Newtonian fluids in dimension three
Kyungkeun Kang, Hwa Kil Kim, Jae-Myoung Kim
We consider the Cauchy problem for coupled system of Vlasov and non-Newtonian fluid equations. We establish local well--posedness of the strong solutions, provided that the initial…
Existence of regular solutions for a certain type of non-Newtonian Navier-Stokes equations
Kyungkeun Kang, Hwa Kil Kim, Jae-Myoung Kim
We are concerned with existence of regular solutions for non-Newtonian fluids in dimension three. For a certain type of non-Newtonian fluids we prove local existence of unique regu…
Infinite horizon value functions in the Wasserstein spaces
Ryan Hynd, Hwa Kil Kim
We perform a systematic study of optimization problems in the Wasserstein spaces that are analogs of infinite horizon, deterministic control problems. We derive necessary condition…
Value functions in the Wasserstein spaces: finite time horizons
Ryan Hynd, Hwa Kil Kim
We study analogs of value functions arising in classical mechanics in the space of probability measures endowed with the Wasserstein metric , for . Our main result…
Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space
Hwa Kil Kim
In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let be a given Hamiltonian satisfying certain properties. We regularize usin…
Generating and Adding Flows on Locally Complete Metric Spaces
Hwa Kil Kim, Nader Masmoudi
As a generalization of a vector field on a manifold, the notion of an arc field on a locally complete metric space was introduced in \cite{BC}. In that paper, the authors proved an…
Optimal transportation, topology and uniqueness
Najma Ahmad, Hwa Kil Kim, Robert J. McCann
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when…
Extremal doubly stochastic measures and optimal transportation
Najma Ahmad, Hwa Kil Kim, Robert J. McCann
This article connects the theory of extremal doubly stochastic measures to the geometry and topology of optimal transportation. We begin by reviewing an old question (# 111) of Bir…
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems
Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
Let M denote the space of probability measures on R^D endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely continuous curves in M was intr…