7. Lecture Room
earlier winter schools
winter school posters
winter school VODs
VOD's for 2013 winter are now availble.
2013 PDE School GuideBook /
2013 PDE School Poster /
Slides of Prof. Mimura /
Slides of Prof. Choe /
Lecture note of Prof. Wang /
Slides of Prof. H.Kim /
Dates: 2013.01.07 - 2013.01.11
Place: KAIST, Daejeon, Korea
Topics: Regularity theory and PDEs from Fluid and Biology
Sponsor: NIMS and KAIST BK21
Registration Period : 2012.10.08 - 2012.11.10
The third Korea PDE school will be held like followings.
Principal lecturers and topics to be discussed
Choe, Hi Jun (Yonsei University, Korea) on "Navier-Stokes equations"
1. Stokes equations and its potentials.
/ 2. Solvability of Stokes boundary value problems.
/ 3. Existence of Navier-Stokes equations.
/ 4. Regularity questions of Navier-Stokes equations.
/ 5. CKN (Caffarelli-Kohn-Nirenberg) result and simplification.
/ 6. Improvement of CKN result
/ 7. Connection between Navier-Stokes and Euler eqautions
Mimura, Masayasu (Meiji University, Japan) on "Application of reaction-diffusion systems to biological and chemical systems"
1. Prologue: Initiation to reaction-diffusion systems
/ 2. Consumer-resource systems I: Combustion under microgravity
/ 3. Consumer-resource systems II: Self-organized patterns in bacterial colonies
/ 4. Nonlinear-nonequilibrium reaction-diffusion systems: Interaction of traveling pulses and spots
/ 5. Competition-diffusion systems: competitive exclusion and competitor-mediated coexistence
Wang, Lihe (University of Iowa, USA) on "Regularity theory for elliptic and parabolic equations"
1. Geometric and physical viewpoints of estimates: The geometric and physical meaning of estimates of PDEs are explained. Basic examples are given.
/ 2. Pointwise estimates: Pointwise Schauder estimates are given for both elliptic and parabolic equations.
/ 3. Pointwise to global estimates: An universal viewpoints are give about pointwise estimates to global regularity theory.
/ 4. Integral estimates: L^p estimats is discussed.
Bae, Myoungjean (Postech) on "Examples of shock solutions for Euler system"
Kang, Kyung-Keun (Yonsei University) on "Global existence of weak solutions for a Keller-Segel-fluid model with
Kim, Hyunseok (Sogang University) on "Mathematical analysis of the stationary motion of an incompressible viscous fluid"
Kim, Yong Jung (KAIST) on "Starvation driven diffusion as a survival strategy of biological organisms"
Li, Tong (University of Iowa, USA) on "Global entropy solutions to a quasilinear hyperbolic system modeling blood flow"