Video

Mixed type PDEs and compressible flow

Extra Form
Lecturer 배명진
Dept. POSTECH
date Apr 11, 2013

If density of flow is globally a constant, then the flow is said incompressible. Otherwise, the flow is said compressible. Flow motion of compressible inviscid flow is governed by Euler system. The Euler system is a nonlinear PDE system describing conservation of mass, momentum and energy. Interestingly, mathematical property of Euler system dramatically changes depending on whether speed of flow exceeds sonic speed or not. In addition, nonlinearity of Euler system can cause a shock or a contact discontinuity/vortex sheet in which physical features of flow discontinuously change. This talk will present mathematical approach to understand such nonlinear physical phenomena. If time allows, some open problems will be discussed as well.

 Subject+ContentSubjectContentCommentUser NameNick NameUser IDTag
1. 2022-1 Rookies Pitch: Symplectic Topology (문지연)

CategoryBK21 FOUR Rookies Pitch Dept.수학연구소 Lecturer문지연
2. How to solve linear systems in practice

There are basically two approaches for solving linear systems: one is to exactly solve the linear sytem such as Gaussian-elimination. The other approximates the solution in the Krylov spaces; Conjugate-gradient and General minimum residual m...
CategoryMath Colloquia Dept.이화여대 수학과 Lecturer민조홍
3. Hybrid discontinuous Galerkin methods in computational science and engineering

Computation facilitates to understand phenomena and processes from science and engineering; we no longer need to depend only on theory and experiment. Computational Science and Engineering (CSE) is a rapidly developing multidisciplinary area...
CategoryMath Colloquia Dept.연세대 Lecturer박은재
4. Infinite order rationally slice knots

A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the se...
CategoryMath Colloquia Dept.카이스트 수리과학과 Lecturer박정환
5. Restriction theorems for real and complex curves

We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박종국
6. 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

Despite of the fact that 4-dimensional manifolds together with 3-dimensional manifolds are the most fundamental and important objects in geometry and topology and topologists had great achievements in 1960's, there has been little known on 4...
CategorySpecial Colloquia Dept.서울대학교 Lecturer박종일
7. 2023-2 Optimization Theory (박지선)

CategoryBK21 FOUR Rookies Pitch Dept.수리과학부 Lecturer박지선
8. Iwasawa main conjecture and p-adic L-functions

The theory of L-functions and zeta functions have been the key subject of mathematical research during the centuries since the Riemann zeta function was introduced and its important connection to the arithmetic of the integer was recognized....
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박지훈
9. Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds

In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...
CategoryMath Colloquia Dept.KIAS Lecturer박진성
10. 2021-1 Rookies Pitch: PDE, Regularity Theory (박진완)

CategoryBK21 FOUR Rookies Pitch Dept.수학연구소 Lecturer박진완
11. Equations defining algebraic curves and their tangent and secant varieties

It is a fundamental problem in algebraic geometry to study equations defining algebraic curves. In 1984, Mark Green formulated a famous conjecture on equations defining canonical curves and their syzygies. In early 2000's, Claire Voisin...
CategoryMath Colloquia Dept.KAIST Lecturer박진형
12. 2021-1 Rookies Pitch: PDE, Dynamical Systems (박한솔)

CategoryBK21 FOUR Rookies Pitch Dept.수리과학부 Lecturer박한솔
13. 2022-2 Rookies Pitch: Algebraic Geometry (박현준)

CategoryBK21 FOUR Rookies Pitch Dept.KIAS Lecturer박현준
14. Seoul ICM 2014 유치과정 개요 및 준비전략

국제수학자대회(ICM, International Congress of Mathematicians)는 1897년 쮜리히에서 처음 개최되었고, 매 4년마다 개최된다. 100여국 4천여 명 정도의 규모로 9일 동안 계속된다. 우리시대 최고의 수학자들이 참여하며, 필즈상(Fields Medal)을 개막식에서 ...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박형주
15. Mixed type PDEs and compressible flow

If density of flow is globally a constant, then the flow is said incompressible. Otherwise, the flow is said compressible. Flow motion of compressible inviscid flow is governed by Euler system. The Euler system is a nonlinear PDE system desc...
CategoryMath Colloquia Dept.POSTECH Lecturer배명진
16. <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations

In this talk, I will briefly introduce some properties of the incompressible Navier-Stokes equations. Then, I will review some classical results obtained by harmonic analysis tools.
CategoryMath Colloquia Dept.UNIST Lecturer배한택
17. Essential dimension of simple algebras

The notion of essential dimension was introduced by Buhler and Reichstein in the late 90s. Roughly speaking, the essential dimension of an algebraic object is the minimal number of algebraically independent parameters one needs to define the...
CategoryMath Colloquia Dept.KAIST Lecturer백상훈
18. 1 is big enough to understand 3

We discuss how the closed connected 1-dimensional manifold, namely the circle, can help understanding 3-manifolds. We describe so-called the universal circle proposed by a lengendary mathematician, William Thurston, and discuss certain gene...
CategoryMath Colloquia Dept.카이스트 Lecturer백형렬