Kihyun Kim

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

• (with Soonsik Kwon and Sung-Jin Oh) Blow-up dynamics for radial self-dual Chern-Simons-Schrödinger equation with prescribed asymptotic profile
  arXiv:2409.13274

• (with Taegyu Kim and Soonsik Kwon) Construction of smooth chiral finite-time blow-up solutions to Calogero–Moser derivative nonlinear Schrödinger equation
  to appear in Mem. Amer. Math. Soc., arXiv:2404.09603

• (with Frank Merle) On classification of global dynamics for energy-critical equivariant harmonic map heat flows and radial nonlinear heat equation
  Comm. Pure Appl. Math. 78 (2025), 1783-1842, arXiv:2404.04247, DOI 10.1002/cpa.22253

• Rigidity of smooth finite-time blow-up for equivariant self-dual Chern-Simons-Schrödinger equation
  J. Eur. Math. Soc. (2025), published online first, arXiv:2210.05412, DOI 10.4171/JEMS/1569

• 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
  Ann. Sci. Éc. Norm. Supér. (4) 57 (2024), no. 6, 1599-1691, arXiv:2010.03252, DOI 10.24033/asens.2596

• (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