56 citations · 204 across the 21 of their papers we have counts for
22 papers
Non-uniqueness of weak solutions to cross-diffusion systems with advection
José A. Carrillo, Ansgar Jüngel, Jakub Skrzeczkowski +1
A cross-diffusion system with advection is considered on the whole line, describing the dynamics of two segregating population species. Starting from two initial densities supporte…
On well-posedness of -SQG equations in the half-plane
In-Jee Jeong, Junha Kim, Yao Yao
We investigate the well-posedness of -SQG equations in the half-plane, where and correspond to the 2D Euler and SQG equations respectively. For , we prov…
Suppression of chemotactic singularity by buoyancy
Zhongtian Hu, Alexander Kiselev, Yao Yao
Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of f…
Small scale formation for the 2D Boussinesq equation
Alexander Kiselev, Jaemin Park, Yao Yao
We study the 2D incompressible Boussinesq equation without thermal diffusion, and aim to construct rigorous examples of small scale formations as time goes to infinity. In the visc…
Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel
José A. Carrillo, David Gómez-Castro, Yao Yao +1
We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and…
Small scale formations in the incompressible porous media equation
Alexander Kiselev, Yao Yao
We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an app…
Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via…
Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity , such that it has positive vo…
Sharp stability for the interaction energy
Xukai Yan, Yao Yao
This paper is devoted to stability estimates for the interaction energy with strictly radially decreasing interaction potentials, such as the Coulomb and Riesz potentials. For a ge…
Chemotaxis and Reactions in Biology
Alexander Kiselev, Fedor Nazarov, Lenya Ryzhik +1
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions. One example is the immune syste…
Uniqueness and non-uniqueness of steady states of aggregation-diffusion equations
Matias G. Delgadino, Xukai Yan, Yao Yao
We consider a nonlocal aggregation equation with degenerate diffusion, which describes the mean-field limit of interacting particles driven by nonlocal interactions and localized r…
Symmetry in stationary and uniformly-rotating solutions of active scalar equations
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we study the radial symmetry properties of stationary and uniformly-rotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch s…
Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
Jose A. Carrillo, Katy Craig, Yao Yao
Given a large ensemble of interacting particles, driven by nonlocal interactions and localized repulsion, the mean-field limit leads to a class of nonlocal, nonlinear partial diffe…
Congested aggregation via Newtonian interaction
Katy Craig, Inwon Kim, Yao Yao
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. Thi…
Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics
J. A. Carrillo, S. Hittmeir, B. Volzone +1
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This…
Finite time singularity formation for the modified SQG patch equation
Alexander Kiselev, Lenya Ryzhik, Yao Yao +1
It is well known that the incompressible Euler equations in two dimensions have globally regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart…
Local regularity for the modified SQG patch equation
Alexander Kiselev, Yao Yao, Andrej Zlatos
We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified SQG equations. These involve a parameter which appears in th…
Mixing and Un-mixing by Incompressible Flows
Yao Yao, Andrej Zlatos
We consider the questions of efficient mixing and un-mixing by incompressible flows which satisfy periodic, no-flow, or no-slip boundary conditions on a square. Under the uniform-i…
Quasi-static evolution and congested crowd transport
Damon Alexander, Inwon Kim, Yao Yao
We consider the relationship between Hele-Shaw evolution with drift, the porous medium equation with superharmonic drift, and a congested crowd motion model originally proposed by…
An aggregation equation with degenerate diffusion: qualitative property of solutions
Lincoln Chayes, Inwon Kim, Yao Yao
We study a nonlocal aggregation equation with degenerate diffusion, set in a periodic domain. This equation represents the generalization to of the McKean-Vlasov equation w…
Asymptotic Behavior for Critical Patlak-Keller-Segel model and an Repulsive-Attractive Aggregation Equation
Yao Yao
In this paper we study the long time asymptotic behavior for a class of diffusion-aggregation equations. Most results except the ones in Section 3.3 concern radial solutions. The m…
The Patlak-Keller-Segel model and its variations: properties of solutions via maximum principle
Inwon Kim, Yao Yao
In this paper we investigate qualitative and asymptotic behavior of solutions for a class of diffusion-aggregation equations. Most results except the ones in section 3 and 6 concer…