16 citations · 34 across the 13 of their papers we have counts for
13 papers
Stability and instability for the fully parabolic Keller-Segel system around constant equilibrium
Jaewook Ahn, Jae-Myoung Kim, Junha Kim
This paper studies the Cauchy problem for the fully parabolic Keller-Segel system. The main results show that there exists a critical threshold for steady states $…
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…
Velocity blow-up in for the 2D Euler equations
Min Jun Jo, Junha Kim
We give a vorticity-dynamical proof of -illposedness of the 2D Euler equations. Our construction shows that the unique Yudovich solution escapes both and i…
Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain
Juhi Jang, Junha Kim
We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under th…
Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator
Min Jun Jo, Junha Kim, Jihoon Lee
We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this e…
Quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation on the three fundamental domains
Min Jun Jo, Junha Kim
We analyze the asymptotic stability of the quasi-linearly stratified densities in the 2D inviscid incompressible porous medium equation on with respect to the buoyancy fre…
Non-convergence of the rotating stratified flows toward the quasi-geostrophic dynamics
Min Jun Jo, Junha Kim, Jihoon Lee
The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid ro…
A revisit to the pressureless Euler--Navier--Stokes system in the whole space and its optimal temporal decay
Young-Pil Choi, Jinwook Jung, Junha Kim
In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler--Navier--Stokes system and the optimal temporal decay rates of…
A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces
In-Jee Jeong, Junha Kim
We provide a simple proof that the Cauchy problem for the incompressible Euler equations in with any is ill-posed in critical Sobolev spaces, extending an…
On Liouville type theorems for the stationary MHD and the Hall-MHD systems in
Dongho Chae, Junha Kim, Jörg Wolf
In this paper we prove a Liouville type theorem for the stationary MHD and the stationary Hall-MHD systems. Assuming suitable growth condition at infinity for the mean oscillations…
On Liouville type theorems in the stationary non-Newtonian fluids
Dongho Chae, Junha Kim, Jörg Wolf
In this paper we prove a Liouville type theorem for the stationary equations of a non-Newtonian fluid in with the viscous part of the stress tensor $\mathbf{A}_p(u)…
Strong illposedness for SQG in critical Sobolev spaces
In-Jee Jeong, Junha Kim
We prove that the inviscid surface quasi-geostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data $H^{2}(\bbT^2)$ without any sol…
Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial
Jungwon Park, Junha Kim, Inkyu Jang +1
This paper presents a new efficient algorithm which guarantees a solution for a class of multi-agent trajectory planning problems in obstacle-dense environments. Our algorithm comb…