Publication and Preprints

• On illposedness of the Hall and electron magnetohydrodynamic equations without resistivity on the whole space (with Sung-Jin Oh)
  arXiv, 36 pp.
  
  
• Wellposedness of the electron MHD without resistivity for large perturbations of the uniform magnetic field (with Sung-Jin Oh)
  arXiv, 58 pp.
  
  
• On global regularity of some bi-rotational Euler flows (with Kyudong Choi and Deokwoo Lim)
  arXiv, 25 pp.
  
  
• Global Cauchy problem for the Vlasov–Riesz–Fokker–Planck system near the global Maxwellian (with Young-Pil Choi and Kyungkeun Kang)
  preprint, 19 pp.
  
  
• Illposedness for dispersive equations: Degenerate dispersion and Takeuchi–Mizohata condition (with Sung-Jin Oh)
  arXiv, 54 pp.
  
  
• Illposedness via degenerate dispersion for generalized surface quasi-geostrophic equations with singular velocities (with Dongho Chae and Sung-Jin Oh)
  arXiv, 74 pp.
  
  
• Well-posedness for Ohkitani model and long-time existence for surface quasi-geostrophic equations (with Dongho Chae, Jungkyoung Na and Sung-Jin Oh)
  arXiv, 21 pp.
  
  
• Twisting in Hamiltonian Flows and Perfect Fluids (with Tarek Elgindi and Theodore Drivas)
  arXiv, 30 pp.
  
  
• On well-posedness of α-SQG equations in the half-plane (with Junha Kim and Yao Yao)
  arXiv, 20 pp.
  
  
• Logarithmic spirals in 2d perfect fluids (with Ayman Said)
  arXiv, 21 pp.
  
  
• Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations (with Jungkyoung Na and Tsuyoshi Yoneda)
  Nonlinearity, to appear, 17 pp. arXiv
  
  
• On vortex stretching for anti-parallel axisymmetric flows (with Kyudong Choi)
  Amer. J. Math., to appear, 27 pp. arXiv
  
  
• Global regularity for some axisymmetric Euler flows in R^d (with Kyudong Choi and Deokwoo Lim)
  Proc. Amer. Math. Soc., to appear, 10 pp. arXiv
  
  
• Strong ill-posedness of SQG in critical Sobolev spaces (with Junha Kim)
  Anal. PDE., 17 (2024), No. 1, 133–170. journal arXiv
  
  
• Well-posedness and singularity formation for Vlasov–Riesz system (with Young-Pil Choi)
  Kinet. Relat. Models, 23 pp. journal arXiv
  
  
• Axi-symmetric solutions active vector models generalizing 3D Euler and electron–MHD equations (with Dongho Chae and Kyudong Choi)
  Nonlinear Anal., RWA 74 (2023), 20 pp. journal arXiv
  
  
• On evolution of corner-like gSQG patches (with Junekey Jeon)
  J. Math. Fluid Mech., 25 (2023), Paper No. 35, 10 pp. journal arXiv
  
  
• Filamentation near Hill's vortex (with Kyudong Choi)
  Comm. Partial Differential Equations, 48 (2023), no. 1, 54–85. journal arXiv
  
  
• Time periodic solutions to a heat equation with linear forcing and boundary conditions (with Sun-Chul Kim)
  J. Korean Math. Soc., 60 (2023), no. 2, 465477. journal
  
  
• On Singular Vortex Patches, I: Well-posedness Issues (with Tarek Elgindi)
  Mem. Amer. Math. Soc., 283(1400):1–102, 2023. journal arXiv
  
  
• Active vector models generalizing 3D Euler and electron–MHD systems (with Dongho Chae)
  Nonlinearity 36 (2023), no. 1, 458–475. journal arXiv
  
  
• Preservation of log-Hölder coefficients of the vorticity in the transport equation (with Dongho Chae)
  J. Differential Equations 343, (2023), 910–918. journal arXiv
  
  
• Global weak solutions to Vlasov–Manev–Fokker–Planck system (with Young-Pil Choi)
  Kinet. Relat. Models (2023), 16(1), 41–53. journal arXiv
  
  
• Stability of monotone vorticities in the half cylinder and infinite perimeter growth for patches (with Kyudong Choi and Deokwoo Lim)
  J. Nonlinear Sci., 32 (2022), no. 6, Paper No. 97. journal arXiv
  
  
• Stability and instability of Kelvin waves (with Kyudong Choi)
  Calc. Var. PDE, 61 (2022), 221, 38 pp. journal arXiv
  
  
• A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces (with Junha Kim)
  J. Funct. Anal., 283 (2022), no. 10, 34 pp. journal arXiv
  
  
• On the Cauchy problem for the Hall and electron magnetohydrodynamic equations without resistivity I: illposedness near degenerate stationary solutions (with Sung-Jin Oh)
  Ann. PDE. 8, 15 (2022), 106 pp. journal arXiv
  
  
• Well-posedness and singularity formation for inviscid Keller–Segel–fluid system of consumption type (with Kyungkeun Kang)
  Comm. Math Phys., 390, 1175–1217 (2022). journal arXiv
  
  
• Anomalous Dissipation in Passive Scalar Transport (with Tarek Elgindi, Theodore Drivas, and Gautam Iyer)
  Arch. Rational Mech. Anal., 243 (2022), no. 3, 1151–1180 journal arXiv
  
  
• Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier–Stokes equations (with Tsuyoshi Yoneda)
  Proc. Amer. Math. Soc., 150 (2022), no. 3, 1279–1286. journal arXiv
  
  
• Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole (with Kyudong Choi)
  Nonlinear Anal., Real World Appl. 65 (2022), Paper No. 103470, 20 pp. journal arXiv
  
  
• On well-posedness and singularity formation for the Euler–Riesz system (with Young-Pil Choi)
  J. Differential Equations, 306 (2022), no 5, 296–332. journal arXiv
  
  
• The incompressible Euler equations under octahedral symmetry: singularity formation in a fundamental domain (with Tarek Elgindi)
  Adv. Math., 393 (2021), Paper No. 108091, 63 pp. journal arXiv
  
  
• Relaxation to fractional porous medium equation from Euler–Riesz system (with Young-Pil Choi)
  J. Nonlinear Sci., 31 (2021), no. 6, Paper No. 95, 12 pp. journal arXiv
  
  
• Loss of regularity for the 2D Euler equations
  J. Math. Fluid Mech., 23 (2021), no. 4, Paper No. 95, 11 pp. journal arXiv
  
  
• Vortex stretching and a modified zeroth law for the incompressible 3D Navier–Stokes equations (with Tsuyoshi Yoneda)
  Math. Ann., (2021), 380(3), 2041–2072 journal arXiv
  
  
• Classical solutions to the fractional porous medium flow (with Young-Pil Choi)
  Nonlinear Anal., 210 (2021), 112393, 13 pp. journal arXiv
  
  
• Enstrophy dissipation and vortex thinning for the incompressible 2D Navier–Stokes equations (with Tsuyoshi Yoneda)
  Nonlinearity, (2021), no. 4, 1837–1853. journal arXiv
  
  
• Growth of perimeter for vortex patches (with Kyudong Choi)
  Appl. Math. Lett, (2021), 106857, 9 pp. journal arXiv
  
  
• On Singular Vortex Patches, II: Long-time dynamics (with Tarek Elgindi)
  Trans. Amer. Math. Soc. 373 (2020), no. 9, 6757–6775. journal arXiv
  
  
• On stationary solutions and inviscid limits for generalized Constantin–Lax–Majda equation with O(1) forcing (with Sun-Chul Kim)
  Nonlinearity 33 (2020), no. 12, 6662–6694 journal
  
  
• Finite-time Singularity Formation for Strong Solutions to the Boussinesq System (with Tarek Elgindi)
  Ann. PDE. 6 (2020), no. 1, Paper No. 5, 50 pp. journal arXiv
  
  
• On the Effects of Advection and Vortex Stretching (with Tarek Elgindi)
  Arch. Rational Mech. Anal. 235 (2020), no. 3, 1763–1817. journal arXiv
  
  
• Symmetries and Critical Phenomena in Fluids (with Tarek Elgindi)
  Comm. Pure Appl. Math. 73 (2020), no. 2, 257–316. journal arXiv
  
  
• On the stationary solutions and inviscid limit for the generalized Proudman–Johnson equation with O(1)–forcing (with Sun-Chul Kim)
  J. Math. Anal. Appl. 472 (2019), no. 1, 842–863 journal
  
  
• Self-similar solutions for dyadic models of the Euler equations
  J. Differential Equations 266 (2019), no. 11, 7197–7204. journal arXiv
  
  
• Finite-time Singularity Formation for Strong Solutions to the axi-symmetric 3D Euler Equations (with Tarek Elgindi)
  Ann. PDE. 5 (2019), no. 2, Paper No. 16, 51 pp journal arXiv
  
  
• Outer Billiards with Contraction: Regular Polygons
  Dyn. Syst. 33 (2018), no. 4, 565–580. journal arXiv
  
  
• Ill-posedness for the incompressible Euler equations in critical Sobolev spaces (with Tarek Elgindi)
  Ann. PDE. 3 (2017), no. 1, Paper No. 7, 19 pp. journal arXiv
  
  
• Discrete Schrödinger equation and ill-posedness for the Euler equation (with Benoit Pausader)
  Discrete Contin. Dyn. Syst. 37 (2017), no. 1, 281–293. journal
  
  
• A Limit theorem for stochastically decaying partitions at the edge (with Sasha Sodin)
  Random Matrices Theory Appl. 5 (2016), no. 4, 1650016, 36 pp. journal arXiv
  
  
• A Blow-Up Result for Dyadic Models of the Euler Equations (with Dong Li)
  Comm. Math Phys. 337 (2015), no. 2, 1027–1034. journal arXiv
  
  
• Outer Billiards with Contraction: Attracting Cantor Sets
  Exp. Math. 24 (2015), no. 1, 53–64. journal arXiv
  
  
• Gale–Robinson sequences and brane tilings (with Gregg Musiker and Sicong Zhang)
  Discrete Math. Theor. Comput. Sci. Proc. (2013) journal