The 10th Korea PDE Winter School

The 10th Korea PDE Winter School will be held as follows.

   Date:  2024. 02. 19. (Mon.)~ 2024. 02. 23. (Fri.)

   Place: KAIST,  E6-1, Rm 1501, Daejeon, Korea

   Topics: Mathematical Theories of Elliptic/Hyperbolic PDEs 

   Organizers: Soonsik Kwon (KAIST), Jihoon Lee(Chung-Ang Univ.)

    Co-Organizer :  SAARC

   Registration Period:  Dec. 5th, 2023 ~ Jan. 10th, 2024

Principal lecturers and lecture topics

Qing Han (University of Notre DAME, USA) will give 5 lectures on "Regularity theory for uniformly degenerate elliptic equations".   (download   lecture notes)

Lecture 1: Introduction and existence of solutions

Lecture 2: Regularity along tangential directions

Lecture 3: Regularity along normal direction

Lecture 4: Expansions near the boundary

Lecture 5: Concise boundary regularity

Bongsuk Kwon (UNIST) and Moon-jin Kang (KAIST) will give 4 lectures on "Formation and stability of singularities arising in compressible fluid flow ".

Bongsuk Kwon will give two lectures with titles "Formation of singularities in compressible fluids I, II".  

lecture note 

Moon-Jin Kang will give two lectures with titles "Riemann problem, stability of Riemann solutions, and inviscid limit from Navier-Stokes equations" and "From Navier-Stokes to small BV entropy solutions to Cauchy problem for 1D Euler" 

lecture note 

Invited Speakers and Talk Titles

Junsik Bae (UNIST) "An Evans function approach to spectral instability of the generalized KdV solitary waves"  slides 

Young-Pil Choi (Yonsei University) "Asymptotic analysis of kinetic models towards the compressible Euler-Poisson equations". slides 

 In-Jee Jeong (Seoul National University) "Small-scale creation in incompressible fluid dynamics " note 

Jeongho Kim (Kyunghee University) "Large-time behavior of viscous-dispersive shock for the Navier-Stokes-Korteweg equations " slides 

Jehan Oh (Kyungpook National University) "Regularity for a class of degenerate/singular fully nonlinear elliptic equations" slides

Jihoon Ok (Sogang University) "Regularity results for uniformly and nonuniformly elliptic equations"  slides

Jinmyeong Seok (Seoul National University) "Modeling of stars in Euler-Poisson equations"  slides

Registration 

등록(Google form)

참가자는 본인 혹은 지도교수의 펀딩을 이용하는 것을 원칙으로 합니다. 모든 참가자에 점심바우처를 제공할 예정입니다.

지도교수의 연구비 지원이 없는 학생이나 연구원 참가자를 위한 제한된 수의 숙박을 준비하고 있습니다. 숙박지원이 필요하신 참가자는 권순식 교수(soonsikk@kaist.edu)에 따로 연락해 주십시요.  

list of registration

Time Table

Contributed Talks

CT1 (Feb, 21 14:00~ 15:00)

        Junho Choi (KAIST) "HOW TO APPLY SPECTRAL METHODS TO MACHINE LEARNING FOR SOLVING PDES"

        Pilgyu Jung (Korea Univ.) "The Fabes-Strook approach to Aleksandrov-Bakelman-Pucci estimates with $L_d$ drift"

         Deokwoo Lim (Seoul National U.) "Global regularity for some axisymmetric Euler flows in higher dimensions"

CT2 (Feb, 21 15:15 ~ 15:55)

         Dowan Koo (Yonsei U.) "Critical thresholds in pressureless Euler--Poisson equations with background states"

         Kiwoong Kwon (Kyungpook Nat. U.) "Relative Entropy Technique for Compressible Motions as Hamiltonian Flows: An Analysis with Respect to Placement and Momentum Maps"

CT3 (Feb. 22 16:30 ~ 17:30)

         Geuntaek Seo (Yonsei U.) "Bounded weak solutions for Keller-Segel equations with generalized diffusion and logistic source via an unbalanced Optimal Transport splitting scheme"

           Chanhong Min (Yonsei U.) "Local and global regularity for the Stokes and Navier-Stokes equations with the localized boundary data in the half-space"

           Jaeyong Shin (UNIST) "Global solutions to the incompressible Navier-Stokes equations using Beltrami flows"

Accommodation 

Lotte city Hotel Daejeon  https://www.lottehotel.com/daejeon-city/ko.html

Toyoko Inn, Daejeon  http://www.toyoko-inn.co.kr/

Hotel Graytone, Dunsan https://graytone.modoo.at/

Abstract

Download the abstracts of the talks