Kihyun Kim

Hi, I was a Ph.D. student at the Department of Mathematical Sciences at KAIST, under the supervision of Prof. Soonsik Kwon. I defended my Ph.D. thesis titled "Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation" on May 25, 2021.
This webpage will no longer be updated. Please find my Google Sites.

Research Interests

I work on the mathematical analysis of nonlinear dispersive equations. I'm particularly interested in the singularity formation of solutions.

Research Stays

• Feb. 18 -- Aug. 22, 2020, Universität Bielefeld, Germany
• Jul. 15 -- Jul. 19, 2019, Korea Institute of Advanced Study, South Korea
• Jan. 21 -- Jan. 25, 2019, Korea Institute of Advanced Study, South Korea
• Jul. 30 -- Aug. 3, 2018, Korea Institute of Advanced Study, South Korea

Talks

• Analysis and PDE Seminar, Feb. 8, 2021, UC Berkeley, via Zoom,
  Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation
• Participating Analysis Seminar, Jan. 29, 2021, UCLA, via Zoom,
  Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation
• PDE Seminar, Jan. 26, 2021, KAIST, via Zoom,
  Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation
• (Internal) Zoom Analysis Seminar, Jul. 15, 2020, Bielefeld University, Bielefeld, Germany,
  Codimension one blow-up solutions to the equivariant self-dual Chern-Simons-Schrödinger equation
• (Internal) Zoom Analysis Seminar, Apr. 22, 2020, Bielefeld University, Bielefeld, Germany,
  On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability
• KMS Annual Meeting, Oct. 26, 2019, Hongik University, Seoul, South Korea,
  On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability
• Seminar, Jul. 15, 2019, KIAS, Seoul, South Korea,
  On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability
• Seminar, May 3, 2019, Chung-Ang University, Seoul, South Korea,
  Construction of pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation
• Workshop on Analysis of Nonlinear Waves, Mar. 8, 2019, KAIST, Daejeon, South Korea,
  Scattering of the defocusing generalized Benjamin-Ono equations
• Workshop for Students in Analysis and PDE, Jul. 12, 2018, Sogang University, Seoul, South Korea,
  Scattering of the defocusing generalized Benjamin-Ono equations

Publications and Preprints

Most preprints are available at arXiv.

1. Kihyun Kim, Soonsik Kwon, and Sung-Jin Oh, Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schrödinger equation
2. Kihyun Kim and Soonsik Kwon, Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schrödinger equation
3. Kihyun Kim and Robert Schippa, Low regularity well-posedness for generalized Benjamin-Ono equations on the circle, to appear in J. Hyperbolic Differ. Equ.
4. Kihyun Kim and Soonsik Kwon, On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability, to appear in Mem. Amer. Math. Soc.
5. Kihyun Kim and Soonsik Kwon, Scattering for defocusing generalized Benjamin-Ono equation in the energy space, Trans. Amer. Math. Soc. 372 (2019), 5011-5067, DOI: https://doi.org/10.1090/tran/7831

TA Experiences

• 16S MAS331 Topology
• 16F MAS102 Calculus II
• 16F MAS441 Lebesgue Integral Theory
• 17S MAS101 Calculus I
• 17S MAS241 Analysis I
• 18S MAS540 Real Analysis
• 19S MAS331 Topology
• 19F MAS250 Probability and Statistics
• 20F MAS250 Probability and Statistics
• 20F MAS441 Lebesgue Integral Theory