Kihyun Kim

Postdoc at IHES (Huawei Young Talents Program fellow)

I'm a postdoc at IHES until July of 2024. Previously, I was a Ph.D. student at the Department of Mathematical Sciences at KAIST, under the supervision of Soonsik Kwon. I defended my Ph.D. thesis titled "Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation" on May 25th, 2021.

Research Interests

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

Upcoming visits

Jun. 2 -- Jun. 21: UC Berkeley

Publications / Preprints

(In preparation) Blow-up dynamics for radial self-dual Chern-Simons-Schrödinger equation with prescribed asymptotic profile (with Soonsik Kwon and Sung-Jin Oh)

(with Taegyu Kim and Soonsik Kwon) Construction of smooth chiral finite-time blow-up solutions to Calogero–Moser derivative nonlinear Schrödinger equation
arXiv:2404.09603
(with Frank Merle) On classification of global dynamics for energy-critical equivariant harmonic map heat flows and radial nonlinear heat equation
arXiv:2404.04247
Rigidity of smooth finite-time blow-up for equivariant self-dual Chern-Simons-Schrödinger equation
to appear in J. Eur. Math. Soc., arXiv:2210.05412
Sharp universal rate for stable blow-up of corotational wave maps
Comm. Math. Phys. 402 (2023), 2387-2463, arXiv:2202.11150, DOI 10.1007/s00220-023-04774-x
(with Soonsik Kwon and Sung-Jin Oh) Soliton resolution for equivariant self-dual Chern-Simons-Schrödinger equation in weighted Sobolev class
to appear in Amer. J. Math., arXiv:2202.07314
(with Soonsik Kwon and Sung-Jin Oh) Blow-up dynamics for smooth finite energy radial data solutions to the self-dual Chern-Simons-Schrödinger equation
to appear in Ann. Sci. Éc. Norm. Supér., arXiv:2010.03252
(with Soonsik Kwon) Construction of blow-up manifolds to the equivariant self-dual Chern-Simons-Schrödinger equation
Ann. PDE 9 (2023), no. 1, Paper No. 6, 129 pp., arXiv:2009.02943, DOI 10.1007/s40818-023-00147-8
(with Robert Schippa) Low regularity well-posedness for generalized Benjamin-Ono equations on the circle
J. Hyperbolic Differ. Equ. 18 (2021), no. 4, 931-984, arXiv:2007.15505, DOI 10.1142/S0219891621500272
(with Soonsik Kwon) On pseudoconformal blow-up solutions to the self-dual Chern-Simons-Schrödinger equation: existence, uniqueness, and instability
Mem. Amer. Math. Soc. 284 (2023), no. 1409, v+128 pp., arXiv:1909.01055, DOI 10.1090/memo/1409
(with Soonsik Kwon) Scattering for defocusing generalized Benjamin-Ono equation in the energy space
Trans. Amer. Math. Soc. 372 (2019), 5011-5067, arXiv:1801.06612, DOI 10.1090/tran/7831