Monday, September 22, 2025

2025-09-24 / 16:00 ~ 17:30

by ()

Classical variational approach of maximizing the kinetic energy with various constraints provides vortex stability in several special cases, but in general this approach fails when the vorticity is concentrated at several points in the fluid domain. This is simply because such configurations are not local kinetic energy maximizers, even when we restrict the admissible class using all the other coercive conserved quantities of fluid motion. In this talk, we present several results on the stability of multi-vortex solutions, obtained by combining classical variational approach with dynamical bootstrapping schemes. We focus on the case of multiple Lamb dipoles weakly interacting with each other. This is based on joint works with Ken Abe, Kyudong Choi, and Yao Yao.

2025-09-25 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: The pluripotential complex Monge-Ampère flows

by 강보우(KAIST)

TBA

2025-09-22 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Modulo flows and Integer flows of signed graphs

by Rong Luo(West Virginia University)

Nowhere-zero flows of unsigned graphs were introduced by Tutte in 1954 as a dual problem to vertex-coloring of (unsigned) planar graphs. The definition of nowhere-zero flows on signed graphs naturally comes from the study of embeddings of graphs in non-orientable surfaces, where nowhere-zero flows emerge as the dual notion to local tensions. Nowhere-zero flows in signed graphs were introduced by Edmonds and Johnson in 1970 for expressing algorithms on matchings, but systematically studied first by Bouchet in 1983. Bouchet also stated a conjecture which occupies a central place in the area of signed graphs: Every flow-admissible signed graph admits a nowhere-zero 6-flow. There is a significant difference in the flows of signed graphs and unsigned graphs. In this talk I will talk about the progress on the development of the flow theory of signed graphs.

2025-09-24 / 16:00 ~ 17:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

2025-09-22 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식: Vanishing viscosity approximation and parabolic scaling for second-order quasilinear degenerate elliptic equations

by 조민서()

Abstract: In this talk, we consider the second-order quasilinear degenerate elliptic equation whose dominant part has the form $(2x - au_x)u_{xx} + bu_{yy} - u_x = 0$, where $a$ and $b$ are positive constants. We first introduce the physical situation that motivates the present analysis in a very brief manner, and then discuss mathematical difficulties involved in the analysis of the problem. The main part of this talk focuses on methods to overcome those difficulties, such as vanishing viscosity approximation and parabolic scaling. - Reference: [1] Chen, G.-Q. and Feldman, M. (2010). Global solutions to shock reflection by large-angle wedges, Ann. of Math. 171: 1019–1134. *Main reference [2] Bae, M., Chen, G.-Q. and Feldman, M. (2009). Regularity of solutions to regular shock reflection for potential flow, Invent. Math. 175: 505–543.

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