Moon-Jin Kang (강문진)

Assistant professor 
Department of Mathematics
Sookmyung Women's University

Address: 100, Cheongpa-ro 47-gil, Yongsan-gu, Seoul, 04310, Korea
Office: 사회교육관 401호

  • Curriculum Vitae
  • Research Interests
  • I am interested in nonlinear PDEs arising in physics (Fluid dynamics; Kinetic theory; Hyperbolic conservation laws, especially shock waves, Euler equations, Navier-Stokes equations), more precisely in well-posed/ill-posed problems, 
    asymptotic analysis (hydrodynamic limit; inviscid limit),
    & applications of optimal transport theory to PDEs, 
    & modeling issues in complex systems arising in biology, network, social science, etc.

  • Publications

  • Preprints: 

    1. Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system (with A. Vasseur and Y. Wang), arXiv:2002.06412

    2. Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems (with A. Vasseur), arXiv:1902.01792

    3. $L^2$-type contraction for shocks of scalar viscous conservation laws with strictly convex flux, arXiv:1901.02969
    4. Dynamics of a spatially homogeneous Vicsek model for oriented particles on the plane (with J. Morales), arXiv:1608.00185

    Published/accepted Articles :

      [29] Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system (with A. Vasseur), J. Eur. Math. Soc. (JEMS), To appear

      [28] Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities (with A. Vasseur), J. Nonlinear Sci., To appear

      [27] Propagation of the mono-kinetic solution in the Cucker-Smale-type kinetic equations (with J. Kim), Commun. Math. Sci. To appear

      [26] Global well-posedness of large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model (with K. Choi, A. Vasseur), J. Math. Pures Appl.To appear

        [25] Inviscid limit to the shock waves for the fractal Burgers equation (with S. Akopian, A. Vasseur), Commun. Math. Sci. To appear

        [24] Contraction for large perturbations of traveling waves in a hyperbolic-parabolic system arising from a chemotaxis model (with K. Choi, Y. Kwon, A. Vasseur), Math. Mod. Meth. Appl. Sci., To appear

        [23] Hydrodynamic limit of the kinetic thermomechanical Cucker-Smale model in a strong local alignment regime (with S.-Y. Ha, J. Kim, W. J. Shim), Commun. Pure Appl. Anal.,
        19(3), 1233-1256 (2020) [pdf]

        [22] $L^2$-contraction for planar shock waves of multi-dimensional scalar viscous conservation laws (with A. Vasseur and Y. Wang), J. Differential Equations, 267, 2737--2791
        [21] A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment, (with A. Figalli), Analysis & PDE. 12, 843866 (2019)

        [20] From the Vlasov-Poisson equation with strong local alignment to the pressureless Euler-Poisson system, Appl. Math. Lett., 79, 85–91 (2018) 
        [19] Global well-posedness of spatially homogeneous Kolmogorov-Vicsek model as a gradient flow (with A. Figalli and J. Morales), Arch. Rational Mech. Anal.(ARMA)227, 869-896 (2018)
        [18] Non-contraction of intermediate admissible discontinuities for 3-D planar isentropic magnetohydrodynamics, Kinetic & Related Models, 11(1) 107-118 (2018)
        [17] $L^2$-contraction for shock waves of scalar viscous conservation laws (with A. Vasseur), Annales de l'Institut Henri Poincare (C) : Analyse non lineaire, 34(1), 139~156 (2017)
        [16] Existence and stability of planar shocks of viscous scalar conservation laws with space-periodic flux (with A.-L. Dalibard), J. Math. Pures Appl., 107(3), 336--366 (2017)
        [15] Criteria on contractions for entropic discontinuities of systems of conservation laws (with A. Vasseur), Arch. Rational Mech. Anal.(ARMA), 222, 343--391 (2016)
        [14] Global Weak Solutions for Kolmogorov–Vicsek Type Equations with Orientational Interactions (with I. M. Gamba), Arch. Rational Mech. Anal.(ARMA), 222, 317--342. (2016)
        [13] Global existence of strong solutions to the Cucker-Smale-Stokes system (with H.-O. Bae, Y.-P. Choi and S.-Y. Ha), J. Math. Fluid Mech., 18, 381--396 (2016), [pdf]
        [12] Dynamics of time elapsed inhomogeneous neuron network model (with B. Perthame and D. Salort), C. R. Math. Acad. Sci. Paris, 353, 1111-1115 (2015). [pdf]
        [11] Emergent dynamics for the hydrodynamic Cucker-Smale system in a moving domain (with S.-Y. Ha and B. Kwon), SIAM J. Math. Anal., 47(5), 3813--3831 (2015). [pdf]
        [10] Asymptotic analysis of Vlasov-type equations under strong local alignment regime (with A. Vasseur), Math. Mod. Meth. Appl. Sci.(M3AS), 25 (11), 2153--2173 (2015) [pdf]
        [9] A hydrodynamic model for the interaction of Cucker-Smale particles and incompressible fluid (with S.-Y. Ha and B. Kwon), Math. Mod. Meth. Appl. Sci.(M3AS), 24, 2311--2359 (2014)
        [8] Contractivity of transport distances for the kinetic Kuramoto equation (with J. A. Carrillo, Y.-P. Choi, S.-Y. Ha and Y. Kim), J. Statistical Physics, 156, pp.395-415 (2014) [pdf]
        [7] Global existence of strong solution for the Cucker-Smale-Navier-Stokes system (with H.-O. Bae, Y.-P. Choi and S.-Y. Ha), J. Differential Equations, 257, pp. 2225--2255 (2014) 
        [6] Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids (with H.-O. Bae, Y.-P. Choi and S.-Y. Ha), DCDS- Series A, 34, 11, pp.4419--4458 (2014) [pdf]
        [5] Fast and slow relaxations to bi-cluster configurations for the ensemble of Kuramoto oscillators (with S.-Y. Ha), Q. Appl. Math., 71, 707-728 (2013) [pdf]
        [4] A class of interacting particle systems on the infinite cylinder with flocking phenomena (with S.-Y. Ha, C. Lattanzio and B. Rubino), Math. Mod. Meth. Appl. Sci.(M3AS), 22, 125008 (2012) [pdf]
        [3] On the basin of attractors for the unidirectionally coupled Kuramoto model in a ring (with S.-Y. Ha)., SIAM J. Appl. Math. 72-5, pp. 1549-1574 (2012)[pdf]
        [2] Time-asymptotic interaction of flocking particles and an incompressible viscous fluid (with H.-O. Bae, Y.-P. Choi and S.-Y. Ha), Nonlinearity 24, 1155 (2012) [pdf]
        [1] Emergent behaviour of a generalized Viscek-type flocking model (with S.-Y. Ha and E. Jeong ), Nonlinearity, 23, 3139 (2010) [pdf]