Research

Research Interest

    Geometric Measure Theory
    Fourier Analysis
    Partial Differential Equations
    Applied Mathematics

Research Papers

    Geometric Measure Theory & Fourier Analysis

   - Pointwise convergence of sequential Schrodinger means, arXiv
        with Chu-Hee Cho, Hyerim Ko and Sanghyuk Lee,
        J. Inequal. Appl., (2023) Paper No. 54.

  - A global space-time estimate for dispersive operators through its local estimate, arXiv
        with Chu-Hee Cho and Jungjin Lee,
        J. Math. Anal. Appl., 514 (2022) no.1, 126255.  

  - Unique continuation for the Schrodinger equation with gradient term, arXiv
        with Ihyeok Seo,
        Proc. Amer. Math. Soc., 146 (2018) no.6, 2555-2562.

    - Note on Nikodym maximal in the variable Lebesgue spaces,
        with Yutae Choi and Jungjin Lee,
        Math. Nachr., 290 (2017) no.2-3, 187-200.

    - Bochner-Riesz means with respect to a generalized cylinder,
        with Yaryong Heo and Chan Woo Yang,
        Integral Equations Operator Theory, 79 (2014) no.1, 1-21.

    - A relation between the X-ray transform estimates and Kakeya problems,
        Ph.D thesis, POSTECH, 2012.

    Dispersive PDE using Harmonic Analysis

    - On local well-posedness of nonlinear dispersive equations with partially regular data, arXiv
        with Yoonjung Lee and Ihyeok Seo,
        J. Differential Equations, 365 (2023) 38-54.

  - Strichartz estimates in Wiener amalgam spaces and applications to nonlinear wave equations, arXiv
        with Seongyeon Kim and Ihyeok Seo,
        J. Funct. Anal., 281 (2021), no.8, 109147.

    - Strichartz and smoothing estimates in weighted L^2 spaces and their applications, arXiv
        with Ihyeok Seo,
        Indiana Univ. Math. J., 70 (2021), no.3, 949-983.

    - On integrability of wave propagator arising from the Liouville-von Neumann equations, arXiv
        with Yoonjung Lee and Ihyeok Seo,
        Arch. Math., 116 (2021) no.3, 345-358.

    - Strichartz estimates for the Schrodinger propagator in Wiener amalgam spaces, arXiv
        with Seongyeon Kim and Ihyeok Seo,
        J. Math. Anal. Appl., 478 (2019) , no.1, 236-248.

    - Strichartz estimates for the magnetic Schrodinger equation with potentials V of critical decay, arXiv
        with Seonghak Kim,
        Comm. Partial Differential Equations, 42 (2017) no.9, 1467-1480. 

    - Strichartz estimates for Schrodinger equations in weighted L^2 spaces and their applications, arXiv
        with Ihyeok Seo,
        Discrete Contin. Dyn. Syst. A, 37 (2017) no.9, 4877-4906.

    - Inhomogeneous Strichartz estimates for Schrodinger's equations, arXiv
        with Ihyeok Seo,
        J. Math. Anal. Appl., 442 (2016) no.2, 715-725.

    - On weighted L^2 estimates for solutions of the wave equation, arXiv
        with Ihyeok Seo,
        Proc. Amer. Math. Soc., 144 (2016) no.7, 3047-3061.

    - Inhomogeneous Strichartz estimates in spherical coordinates for the fractional Schrodinger equation, arXiv
        with Chu-Hee Cho and Ihyeok Seo,
        Discrete Contin. Dyn. Syst. A, 36 (2016) no.4, 1905-1926.

    - Global well-posedness for higher-order Schrodinger equations in weighted L^2 spaces, arXiv
        with Ihyeok Seo,
        Comm. Partial Differential Equations, 40 (2015) no.10, 1815-1830.

    - Improved inhomogeneous Strichartz estimates for the Schrodinger equation,
        J. Math. Anal. Appl., 373 (2011) no.1, 147-160.

    Partial Differential Equations

  -  Aggregation and volume filling in one-dimensional population dynamics under Dirichlet boundary condition,
        with Hyung Jun Choi and Seonghak Kim,
        submitted. 

  - Two-phase solutions for one-dimensional non-convex elastodynamics, arXiv
        with Seonghak Kim,
        Arch. Ration. Mech. Anal., 232 (2019) no.1, 489-529.

    - The Minkowski dimension of interior singular points in the incompressible Navier-Stokes equations, arXiv
        with Minsuk Yang,
        J. Differential Equations, 261 (2016) no.6, 3137-3148.

    - Dispersive estimates for the Navier-Stokes equations in the rotational framework,
        with Sanghyuk Lee and Ryo Takada,
        Adv. Differential Equations, 19 (2014) no.9-10, 857-878.

    - Strichartz estimates for the Euler equations in the rotational framework,
        with Sanghyuk Lee and Ryo Takada,
        J. Differential Equations, 256 (2014) no.2, 707-744.

    Numerical Analysis & Applied Mathematics

    -  Time splitting method for nonlinear Schrodinger equation with rough initial data in L^2, arXiv
        with Hyung Jun Choi and Seonghak Kim,
        submitted. 

    - Convergence analysis of the splitting method to the nonlinear  heat equation, arXiv
        with Hyung Jun Choi and Woocheol Choi,
        Numer. Methods Partial Differential Equations, 39 (2023) no.4, 3417-3440. 

    - On the splitting method for the nonlinear Schrodinger equation with initial data in H^1, arXiv
        with Woocheol Choi,
        Discrete Contin. Dyn. Syst. A, 41 (2021) no.8, 3837-3867.

    - A finite element method for elliptic optimal problem on a non-convex polygon with corner singularities,
        with Hyung Jun Choi and Woocheol Choi,
        Comput. Math. Appl., 75 (2018) no.1, 45-58.

Papers in Mathematics Education

    -  피자를 합리적으로 나누는 방법 (How to divide a pizza in a rational way), journal
        with Taehoon Kim, Junseok Lee, Jeha Park and Ilho Shin,
과학영재교육 (J. Science Edu. Gifted), 10 (2018), No.3, 260-266.