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Event/News since 2022
2025.12.19 PDE Seminar talk : Woo Jae Lee (Yonsei University) 10:00~11:00, 108-320
Title: Chemotaxis Systems and Singularity Formation
Abstract: In this talk, we introduce chemotaxis systems that describe the movement of cells in response to environmental chemical substances. We compare the Keller-Segel equation and the hyperbolic- parabolic chemotaxis (HPC) system with respect to Vessel formation. Finally, we discuss singularity formation in the HPC system. .
2025.11.21 PDE Seminar talk : JaeYong Shin (Yonsei University) 11:00~12:00, 108-319
Title: Leray Weak Solutions for the Incompressible Navier-Stokes and Hall MHD Equations
Abstract: In this talk, we will discuss Leray weak solutions for the incompressible Navier-Stokes (NS) equations and for the Hall magnetohydrodynamic (Hall MHD) equations. We begin with a brief review of the notion of Leray weak solutions for the NS equations and several of their fundamental properties based on Jean Leray’s seminal 1934 work, including eventual and almost-everywhere regularity, as well as asymptotic behavior. We will then present corresponding results for the Hall MHD equations, based on a joint work with Jinwook Jung (Hanyang University).
2025.11.03 Prof. Akitaka Matsumura's lecture series(11/3-11/5)
Lecture 1. Standard energy methods
Lecture 2. Sophisticated energy methods for small data
Lecture 3. Time weighted energy method
2025.10.28 Prof. I-Kun Chen's lecture series(10/28, 10/30, 11/11, 11/12, 11/13)
Title : Introduction to the Boltzmann Equation ; Grad's Cutoff and Linearization of the Boltzmann Equation.
2025.07.15 PDE Seminar talk : JaeYong Shin (Yonsei University) 11:00~12:00, 108-320
Title: Well-Posedness and Special Solutions in Hall MHD : A Revisit of My Thesis
Abstract: In this talk, I will revisit my Ph.D. thesis, focusing on the well-posedness and special solutions
in the Hall magnetohydrodynamics (Hall MHD) system. Based on my thesis work, my collaborators and
I have developed two related directions of research.
In the first part of the talk, we introduce the concept of the magneto-vorticity field and its regularity.
Using this regularity, we show that the Hall MHD with 2D variables is globally wellposed, provided that only the vertical component of the initial current density is sufficiently small.
In the second part, we discuss double Beltrami states in the Hall MHD. We first examine the double
Beltrami states as a special class of steady solutions to the ideal Hall MHD, closely related to Beltrami
flows in incompressible fluid dynamics. We then extend our analysis to time-dependent double Beltrami
states in the viscous and resistive Hall MHD, exploring their exact form and stability properties.
2025.07.09 PDE Seminar talk : Jeongsu Kyeong (Syracuse University) 11:00~, 108-320
Title: The Neumann Problem for the bi-Laplacian in Infinite Sectors
Abstract: The study of boundary value problems associated with the bi-Laplacian operator $\Delta^{2}$
has attracted over the years a great deal of mathematical interest and this plays an important role in the
theory of elasticity, specifically in the Kirchhoff-Love theory of thin plates. The goal of this talk is to
investigate the solvability and spectral properties of the $L^{p}$ Neumann problem for the bi-Laplacian,
for $p\in(1,\infty)$, in infinite sectors in two dimensions, using singular integral operators and Mellin
transform techniques.
This is joint work with Irina Mitrea (Temple University) and Katharine Ott (Bates College).
2025.07.07-11 Paris-Seoul Joint Workshop on Fluid Dynamics 2025 : 09:00~18:00, École normale supérieure
(co-organized by Prof. Kyudong Choi )
https://sites.google.com/view/paris-seoul-fluid-2025/home?authuser=0
2025.06.16-18 Lecture series on dynamical system : 09:00~18:00, 108-320
(co-organized by Prof. Bongsuk Kwon )
2025.06.05 PDE 2025-1 Mathematical Sciences Colloquium : Inbo Sim (Ulsan University) 16:00~17:15, 108-320
Title: Boundedness of solutionsfor generalized Schr \"{0}dinger-type double phase problems in $\R^N$ and its
applications
2025.05.29 PDE Seminar talk : Deokwoo Lim (Seoul National University) 10:00~11:30, 108-320
Title: On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl
2025.05.22 PDE 2025-1 Mathematical Sciences Colloquium : Jihoon Ok (Sogang University) 16:00~17:15, 108-320
Title: Regularity theory for local and nonlocal elliptic equations
2025.04.25 2025 UNIST Student Research Presentation : 09:30~15:40 ,108-320
1st session(09:30~10:20) : Speaker : Yunjoo Kim
Title : What regularity does the solution have when its gradient blows up?
2nd session(10:30~10:50) : Speaker : Seongnyeong Han
Title : Finite energy velocity from mean-zero vorticity in 2D incompressible Euler equations
3rd session(13:00~13:40) : Speaker : Hwangyoung Choi
Title : Blow up in Chemotaxis system with logistic growth restriction
4th session(13:50~14:15) : Speaker : Yejin Jeong
Title : The minimax method
5th session(14:25~14:50) : Speaker : Haechan Jang
Title : An Introduction to Regularity Theory for Elliptic PDEs
6th session(15:00~15:20) : Speaker : Jaeyoon Lee
Title : Topological Degree Theory
7th session(15:30~15:40) : Speaker : Minsu Jang
Title : self-introduction : My Motivation for PDE
2025.03.13 PDE 2025-1 Mathematical Sciences Colloquium : Jamin Park(Yonsei University), 16:00~17:15 108-320
Title : Absence pf Anomalous Dissipation for Incompressible Fluids
2025.01.06~10 The 11th Korea PDE Winter School (co-organized by Prof. Bongsuk Kwon )
2025.01.03 PDE Seminar talk
(14:00) Minjun Jo (Duke University)
Title: Cusp formation in vortex patches
2024.11.22 Prof. Hantaek Bae's lecture series(4th Session) : Introduction to Fourier Analysis , 10:00~12:00
2024.11.08 Prof. Hantaek Bae's lecture series(3rd Session) : Introduction to Fourier Analysis , 10:00~11:30
2024.10.23~25 2024 UNIST Workshop on the Introduction to the Theory of Elliptic PDEs (organized by Prof. Youngae Lee)
2024.10.17~18 2024 UNIST Workshop on Nonlinear Partial Differential Equations
(organized by Prof. Hantaek Bae)
2024.10.11 Prof. Hantaek Bae's lecture series(2nd Session) : Introduction to Fourier Analysis , 10:30~
2024.10.10 PDE 2024-2 Mathematical Sciences Colloquium : Jehan Oh(Kyungpook National University), 16:00~
Title : Regularity for Non-Uniformly Elliptic Problems
2024.09.27 Prof. Hantaek Bae's lecture series(1st Session) : Introduction to Fourier Analysis , 10:30~
2024.09.05 PDE 2024-2 Mathematical Sciences Colloquium : Junha Kim( Ajou University), 16:00~
Title: Strong Convergence of the Solutions to the Euler-Maxwell Equations as the Speed of Light Tends to Infinity
Abstract: We consider the convergence and non-convergence of smooth solutions of the Euler-Maxwell
equations to the corresponding smooth solutions of the magnetohydrodynamics as the speed of light
tends to infinity. To understand this result, we employ some linear ODE systems with a parameter and
show the convergence and non-convergence of solutions as the parameter goes to infinity. Then, we
briefly prove the convergence and nonconvergence of the Euler-Maxwell equations to the MHD equations.
2024.09.03~ 2024 Fall semester PDE reading seminar (9/03, 9/10, 10/08, 11/05, 11/12, 11/19)
Book : Minimax Methods in Critical Point Theory with Applications to Differential Equations-Paul H. Rabinowitz
1st session(9/03) : Speaker : Yejin Jeong
Title : The Mountain Pass Theorem and its Application for Semilinear Elliptic PDE
Abstract : The concept of the critical point is closely related with the weak solution of a semilinear elliptic PDE. We discussed about the mountain pass theorem, one of the minimax theory, to find the existence of a critical point. In the second part of the talk, we found how to use the mountain pass theorem to find the weak solution, further the classical solution of the semilinear elliptic PDE.
2nd session(9/10) : Speaker : Youngjin Sim
Title : The Application of the Mountain Pass Theorem for Semilinear Elliptic PDE
Abstract : Last time, we studied the mountain pass theorem to find the existence of weak solutions for semilinear elliptic PDE. We discussed more about it this time. We discussed the existence of solutions for more semilinear elliptic PDEs and studied how they have at least two distinct solutions.
3rd session(10/08) : Speaker : Hwangyoung Choi
Title : Some Variants of the Mountain Pass Theorem
Abstract : We can constuct the variants of the minimax equations to find the critical points. We studied how to prove those variants have same conclusions and consequently weaken the (I1) condition for the mountain pass theorem. We also discussed how to construct the 1D example for the variant.
4th session(11/05) : Speaker : Jaeyun Lee
Title : The Saddle Point Theorem and its apllications
Abstract : We presented and proved the Saddle Point Theorem. To prove this theorem, we introduced the Brouwer Degree, which is the index of a solutions of equation on an open set. We also discussed its applications for proving existence of a weak solution of PDEs under certain conditions.
5th session(11/12) : Speaker : Haechan Jang
Title : A generalization of the Mountain Pass Theorem
Abstract : We suggested the generelized version of the Mountation Pass Theorem, via consider weaker condition. By using deformation theorem we can prove theorem. And we applied this theorem to solve the existense problem of PDE system, which can not be applied the saddle point theorem or mountaion pass theorem directly.
6th session(11/19) : Speaker : Yunjoo Kim
Title : The critical point theorem which unifies the Mountain pass theorem and Saddle point theorem.
Abstract : The previous theorems can be applied only if we have finite subspace which is useful enough. We generalize those theorems to handle the cases where the space consists of the direct sum of two infinite dimensional spaces. To verify this, we bring in the generalized degree theory and introduce the concept of link. By using this, we state the new theorem and prove it.
2024.08.28 PDE Seminar talk
(14:30)Jeongho Kim(Kyeong Hee University )
Title: Navier-Stokes-Korteweg System
2024.08.22 PDE Seminar talk
(14:00)Kihoon Seong(Cornell University )
Title: Gaussian fluctuation of Euclidean Φ⁴ QFT
Abstract: I will discuss the asymptotic expansions of the Euclidean Φ⁴-measure in the low-temperature regime. Consequently, we derive limit theorems, specifically the law of large numbers and the central limit theorem for the Φ⁴-measure in the low-temperature limit. In the second part of the talk, I will focus on the infinite volume limit of the focusing Φ⁴-measure. Specifically, with appropriate scaling, the focusing Φ⁴- measure
exhibits Gaussian fluctuations around a scaled solitary wave, that is, the central limit theorem. This talk is based on joint works with Benjamin Gess, Pavlos Tsatsoulis, and Philippe Sosoe.
(16:00)Kichan Bae (Seoul National University )
Title: Control and convergence of Vorticity of Boltzmann equation in High Reynolds number limit
Abstract: We prove the hydrodynamic limit of the 2D Boltzmann equation to the incompressible Euler equation in a periodic box. The main obstacle is that the Boltzmann equation cannot be closed using only its energy
estimate. Additionally, the macroscopic equation has a divergence of velocity with a singular scale 1/epsilon, which does not allow us to utilize the estimate of the macroscopic equation. These problems can be addressed by applying the maximum principle for the vorticity equation using the scaled Navier-Stokes equation. This is joint work with Chanwoo Kim.
2024.07.25 PDE Seminar talk
(10:00)Sungjin Oh(UC Berkeley)
Title: Late time tail of waves on dynamic asymptotically flat spacetimes of odd space dimensions
(11:00)Injee Jung(Seoul Nat'l Univ.)
Title: Global Cauchy problem for the Vlasov–Riesz–Fokker–Planck system near the global Maxwellian
2024.07.15 PDE Mathematical Sciences Colloquium : Chanwoo Kim(Univ. of Wisconsin-Madison)
Title: From Boltzmann to Incompressible Euler
Abstract: In this lecture, we will discuss the formal/mathematical connection between the Boltzmann equation and the incompressible Euler equation. First, we explore a formal expansion of Boltzmann and derive the Navier-Stokes equation with vanishing viscosity, along with an additional forcing term representing microscopic contributions. Second, we provide a brief overview of the mathematical analysis that establishes the convergence of the Boltzmann equation to the incompressible Euler equations. This lecture is accessible to graduate students.
2024.05.30 PDE 2024-1 Mathematical Sciences Colloquium : Ildoo Kim(Department of Mathematics, Korea University)
A Short History for Lp-Theories to Stochastic Partial Differential Equations
2024.05.28 (5/28, 6/4) Dr. Wanyong Shim's lecture series : Conservation laws of Hyperbolic Partial Differential Equations
2024.05.23 PDE 2024-1 Mathematical Sciences Colloquium : Hyung Ju Hwang(Department of Mathematics, POSTECH)
Neural PDE Solvers toward Digital Twin : Theory and Applications
2024.03.26 (03.26-03.29) Nonlinear Wave Workshop
2024.03.22~ 2024 Spring semester PDE reading seminar (3/22, 4/12, 4/26, 5/3, 5/10, 5/17)
Book : Hyperbolic Partial Differential Equations (Serge Alinhac)
1st session(3/22) : Speaker : Yejin Jeong
Title : Introduction to the Hyperbolic Partial Differential Equations
Abstract : We study about the existence and uniqueness of solution of first order strictly hyperbolic system.
2nd session(4/12) : Speaker : Youngjin Shim
Title : Conservation Laws in One-Space Dimension
Abstract : We introduce the definition of admissible Shock and its example. Also, we study the concept of Rarefaction waves and Riemann Invariants.
3rd session(4/26) : Speaker : Jeongsik Yoon
Title : Shock Curves of the Hyperbolic PDE system
Abstract : We talk about the necessary conditions of Shock Curves on Hyperbolic PDE system and Rankine- Hugoniot & Lax condition. Especially, we introduce 'Entropy' to explain the connection between 'physically admissible' solution and Lax condition.
4th session(5/03) : Speaker : Haechan Jang
Title : The solution of Multi-dimensional Wave equation
Abstract : We find the general solution of two- and three-dimensional Wave equation, and using this, study Huygens principle. We also talk about large time decay of the solution.
5th session(5/10) : Speaker : Hwangyoung Choi
Title : Geometry of The Wave Equation
Abstract : We study the 'vector field method' of wave equation and Klainerman's inequality, which are the famous methods to find the decay rate of wave equation's solution.
6th session(5/17) : Speaker : Yunjoo Kim
Title : Energy Inequalities for the Wave Equation
Abstract : We check that several properties of homogeneous wave equations can be applied to the variable- coefficient wave equations, for example, 'Finite speed of propagation', using energy inequality.
2024.03.08 PDE Seminar talk : Minjun Jo (Duke University ) : Discussion on the regularity and the singularity in the fluid equations with/without the viscosity effect
2023.12.08 2023 Mini Workshop on Nonlinear PDEs from Fluid Mechanics
https://sites.google.com/view/mini-workshop-on-nonlinear-pde/home
2023.11.24 Dr. Junsik Bae's lecture series : Solitary waves of the Euler-Poisson system
2023.11.24 Dr. Sang-Hyuck Moon's lecture series : Nonlinear elliptic partial differential equations and systems
2023.11.17 PDE 2023-2 Mathematical Sciences Colloquium : Hyunseok Kim(Sogang University)
2023.10.13 Dr. Kwan Woo's lecture series I, II : Introduction to Lp theory
2023.10.06 Dr. Dongkwang Kim's lecture series I, II : Blow-up of solutions of semilinear heat equations
2023.09.22 (9/22, 10/6, 10/13, 11/3, 11/10, 11/17) 2023 Fall semester PDE reading seminar organized by Jaeyong Shin and Yunjoo Kim
Book : 1. The Three Dimensional Navier-Stokes Equations (Robinson, Rodrigo, Sadowski)
2. Harmonic Analysis Tools for Solving the Incompressible Navier-Stokes equations (Cannone)
3. Nonlinear Partial Differential Equations; Asymptotic Behavior of Solutions and Selfsimilar Solutions (Giga, Giga, Saal)
2023.09.07 PDE 2023-2 Mathematical Sciences Colloquium : Joerg Wolf(Chung-Ang University )
2023.09.06 PDE Seminar talk : Masahiro Suzuki(Nagoya Institute of Technology )
2023.09.01 Dr. Dongkwang Kim and Dr. Kwan Woo joined our group as a postdoctoral researcher.
2023.08.31 (08.31-09.03) The 5th workshop on recent development of mathematical fluid dynamics and hyperbolic conservation laws
https://sites.google.com/view/the5thworkshoponrecentdevelop/home
2023.08.31 PDE 2023-2 Mathematical Sciences Colloquium : Ohsang Kwon(Chungbuk National University)
2023.08.16 (08.16-08.17) 2023 Summer PDE Workshop
2023.07.25 PDE Seminar talk : Hsin-Yuan Huang(National Yang Ming Chiao Tung University ) : Recent progress on the Liouville systems
2023.07.24 (07.24-07.27) July 24-27 (2023) Recent Progress on Mathematical Fluid Dynamics
https://sites.google.com/view/2023-summer-pde-fluid-jeju/home
2023.07.13 (07.13-07.14) Graduate Students Workshop on the Analysis of PDEs by Yonsei University (UNIST PDEs Graduate Students attended)
2023.06.16 PDE Seminar talk : Eunkyung Ko(Keimyung University ) : Existence of multiple positive solutions for elliptic equations
2023.04.17 (04.17-04.18) Spring UNIST PDE Group Workshop with A. Kiselev
2023.03.03 (3/17, 3/24, 3/31, 4/7, 5/12, 5/19) 2023 Spring semester PDE reading seminar organized by Deokwoo Lim and Wanyong Shim
book : The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction (by Jacob Bedrossian and Vlad Vicol)
2023.02.20 (02.20-02.21) UNIST-Yonsei PDE Graduate students Workshop organized by Prof. Bongsuk Kwon
2023.01.30 (01.30-02.02) 2023 Winter Workshop on Mathematical Analysis of Fluids <Site>
2023.01.30 PDE Seminar talk : Masahiro Suzuki(Nagoya Institute of Technology) : Stability and instability of plasma boundary layers
2023.01.11 Dr. Tania Biswas's lecture : Optimal transportation problems for the Cahn-Hilliard-Navier-Stokes system
2023.01.01 Dr. Tania Biswas joined our group as a postdoctoral researcher.
2022.11.16 PDE Seminar talk : Seonghyeon Jeong(NCTS) : Optimal transportation problems and its relation to the Monge-Ampere equations
2022.11.03 PDE 2022-2 Mathematical Sciences Colloquium : Jinmyoung Seok(Seoul Univ.)
2022.10.24 PDE Seminar talk : Duksoon Oh(CNU) : Multigrid Methods for Vector Field Problems
2022.10.14 PDE 2022-2 Mathematical Sciences Colloquium : Injee Jeong(Seoul Univ.)
2022.10.07 Dr. Ky Ho's lecture series IV : Eigenvalue problems, the maximum principle, regularity, symmetry
2022.09.30 Dr. Ky Ho's lecture series III : Critical $p$-Laplace equations, the Pohozaev's identity, the concentration compactness principle
2022.09.23 Dr. Ky Ho's lecture series II : Investigating the existence of subcritical $p$-Laplace equations via variational methods: the direct methods, using the Mountain Pass Theorem
2022.09.16 Dr. Ky Ho's lecture series on Elliptic PDEs- I : Definition of elliptic PDEs, Sobolev spaces and embeddings
2022.08.30 Dr. Ky Ho joined our group as a postdoctoral researcher.
2022.08.23 PDE Seminar talk (3PM~5PM, Zoom) : Chanwoo Kim(UW-Madison) : From the Boltzmann to the incompressible Euler
2022.08.17 PDE Seminar talk : Doheon Kim(Hanyang Univ.) : A unified framework for distributed optimization algorithms over time-varying directed graphs
2022.08.17 PDE Seminar talk : Jinwook Jung(SNU) : On the Cauchy problem for the pressureless Euler-Navier-Stokes system in the whole space
2022.08.01~03 2022 Summer UNIST/SNU Fluid PDEs Workshop supported partly by BRL
2022.07.25 PDE Seminar talk : Moonjin Kang(KAIST) : Large time behavior of the 1D barotropic Navier-Stokes flows perturbed from Riemann data
2022.07.01 PDE One day workshop supported by BRL
2022.06.29 PDE Seminar talk : Hyunwoo Kwon(Sogang Univ.) : Elliptic equations with singular drifts
2022.06.22 PDE Seminar talk : Sung-Jin Oh(U.C.Berkeley) : A tale of two tails
2022.05.30 PDE Seminar talk : Dohyun Kwon(Univ. of Wisconsin) : Crystalline mean curvature flow with a volume constraint.
2022.03.04 PDE Graduate students workshop
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