Moon-Jin Kang (강문진)

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)

Publications

Preprints: 

1. Time-asymptotic stability of generic Riemann solutions for compressible Navier-Stokes-Fourier equations  (with A. Vasseur and Y. Wang) arXiv:2306.05604

2. From Navier-Stokes to BV solutions of the barotropic Euler equations (with G. Chen and A. Vasseur) arXiv:2401.09305

3. Long-time behavior towards viscous-dispersive shock for Navier-Stokes equations of Korteweg type (with S. Han, J. Kim and H. Lee) arXiv:2402.09751

4. L^2 decay for large perturbations of viscous shocks for multi-D Burgers equation (with H. Oh) arXiv:2403.08445

Published/accepted Articles :

[36]  Large-time behavior of composite waves of viscous shocks for the barotropic Navier-Stokes equations (with S. Han and J. Kim) SIAM Math. Anal. 55, 5526-5574 (2023)

[35]  Dynamics of a spatially homogeneous Vicsek model for oriented particles on the plane (with J. Morales) Anal. Appl. 21, 1251-1273 (2023)

[34]  Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equation (with A. Vasseur and Y. Wang) Adv. Math. 419 (2023)

[33]   Well-posedness of the Riemann problem with two shocks for the isentropic Euler System in a class of vanishing physical viscosity limits (with A. Vasseur) J. Differ. Equat. 338, 128-226 (2022) 

[32] 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), Commun. Math. Phys. 384, 1751–1782 (2021) https://doi.org/10.1007/s00220-021-04100-3 [pdf] 

[31] 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), Invent. Math., 224(1), 55-146 (2021) https://doi.org/10.1007/s00222-020-01004-2  [pdf]

[30] L^2-type contraction for shocks of scalar viscous conservation laws with strictly convex flux, J. Math. Pures Appl., 145, 1-43 (2021) [pdf]

[29] Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system (with A. Vasseur), J. Eur. Math. Soc. (JEMS), 23(2), 585-638 (2021) [pdf]

[28] Inviscid limit to the shock waves for the fractal Burgers equation (with S. Akopian, A. Vasseur), Commun. Math. Sci. 18, 1477-1491 (2020)

[27] Propagation of the mono-kinetic solution in the Cucker-Smale-type kinetic equations (with J. Kim), Commun. Math. Sci. 18, 1221-1231 (2020)

[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., 142, 266-297 (2020)

[25] Global smooth solutions for 1D barotropic Navier-Stokes equations with a large class of degenerate viscosities (with A. Vasseur), J. Nonlinear Sci., 30, 1703--1721 (2020) [pdf]

[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., 30, 387-437 (2020)

[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 large planar shock waves of multi-dimensional scalar viscous conservation laws (with A. Vasseur and Y. Wang), J. Differential Equations, 267, 2737--2791 (2019)

[21] A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment, (with A. Figalli), Analysis & PDE. 12, 843–866 (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]