6 citations · 23 across the 12 of their papers we have counts for
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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…
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…
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…