Research

Research Area: Partial Differential Equations (PDEs)

Well-posedness and Regularity of Viscous Fluid Equations
Transport Equations with Nonlocal Velocity
Coupled system with Fluid Equations
Free boundary problem

Papers

H. Bae. Global well-posedness of the dissipative quasi-geostrophic equations in critical spaces, Proc. Amer. Math. Soc. 136 (2008), 257-261.

H. Bae. Solvability of the free boundary problem of the Navier-Stokes equations with surface tension, Discrete Contin. Dyn. Syst. 29 (2011), 769-801.

H. Bae. Global well-posedness for the critical quasi-geostrophic equations in L^{\infty}, Nonlinear Anal. 75 (2011), 1995-2002.

H. Bae. Global well-posedness for the Keller-Segel system of equations in ciritical spaces, Adv. in Differential Equations and Control Processes 7(2011), no.2, 93-112.

H. Bae, A. Biswas, E. Tadmor. Analyticity of the Navier-Stokes equations in critical Besov spaces, Arch. Ration. Mech. Anal. 205 (2012), no.3, 963-991.

D. Wei, E. Tadmor, H. Bae. Critical threshold in multi-dimensional Euler-Poisson equations with radial symmetry, Commun. Math. Sci. 10 (2012), no.1, 75-86.

H. Bae, K. Trivisa. On the Doi model for the suspensions of rod-like molecules in compressible fluids, Mathematical Models and Methods in Applied Sciences 22 (2012), no. 10, 39pp.

H. Bae, K. Trivisa. On the Doi model for the suspensions of rod-like molecules: global-in-time existence, Commun. Math. Sci. 11 (2013), no.3, 831-850.

H. Bae, R. Granero-Belinchon. Global existence for some transport equations with nonlocal velocity, Adv. Math. 269 (2015), 197-219.

H. Bae. Existence and Analyticity of Lei-Lin Solution to the Navier-Stokes Equations, Proc. Amer. Math. Soc. 143 (2015), no. 7, 2887–2892.

H. Bae, A. Biswas. Gevrey regularity for a class of dissipaive equations with analytic nonlinearity, Methods and Applications of Analysis 20 (2015), No.4, 377-408.

H. Bae, M. Cannone. Log-Lipschitz regularity of the Navier Stokes equations, Nonlinear Analysis 135 (2016), 223-235.

H. Bae, S. Ulusoy. Global well-posedness for nonlinear nonlocal Cauchy problems arising in elasticity, Electron. J. Differential Equations, Vol. 2017 (2017), No. 55, 1-7.

H. Bae, D. Chae, H.Okamoto. On the well-posedness of various one-dimensional model equations for fluid motion. Nonlinear Analysis 169 (2017), 25-43.

H. Bae, K. Kang, S. Kim. Uniqueness of solutions for Keller-Segel system of porous medium type coupled to fluid equations. Journal of Differential Equations 265 (2018) 5360-5387.

H. Bae, R. Granero-Belinchon, O. Lazar. Global existence of weak solutions to dissipative transport equations with nonlocal velocity. Nonlinearity 31 (2018) 1484-1515.

H. Bae. Analyticity of the inhomogeneous incompressible Navier-Stokes equations. Appl. Math. Lett. 83 (2018), 200–206.

H. Bae, K. Kang. Regularity condition of the incompressible Navier-Stokes equations in terms of one velocity component. Appl. Math. Lett. 94 (2019), 120-125.

H. Bae, R. Granero-Belinchon, O. Lazar. On the local and global existence of solutions to 1D transport equations with nonlocal velocity. Netw. Heterog. Media. 14 (2019), No. 3, 471-487.

H. Bae, W. Lee, J. Shin. A blow-up criterion for the inhomogeneous incompressible Euler equations. Nonlinear Anal. 196 (2020), 111774

H. Bae. Analyticity of solutions to the barotropic compressible Navier-Stokes Equations. Journal of Differential Equations 269 (2020) 1718-1743.

H. Bae. Global existence of solutions to some equations modeling phase separation of self-propelled particles. SN Partial Differ. Equ. Appl. 1, 47 (2020).

H. Bae, R. Granero-Belinchon. Global existence and exponential decay to equilibrium for DLSS-type equations. Journal of Dynamics and Differential Equations (2021).

H. Bae, J. Kelliher. Propagation of regularity of level sets for a class of active transport equations. J. Math. Anal. Appl. 497 (2021), no. 1, 124823.

H. Bae, K. Kang. On the existence of unique global-in-time solutions and temporal decay rates of solutions to some non-Newtonian incompressible fluids, Zeitschrift für angewandte Mathematik und Physik, 72, Article number: 55 (2021).

H. Bae. Blow-up conditions of the incompressible Navier-Stokes equations in terms of sequentially defined Besov spaces. Proc. Amer. Math. Soc. 149 (2021), 4379-4385.

H. Bae, R. Granero-Belinchon. Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems. Monatshefte für Mathematik, Monatsh Math (2022).

H. Bae, W. Lee, J. Shin. Gevrey regularity and finite time singularities for the Kakutani-Matsuuchi model. Nonlinear Anal. Real World Appl. 63 (2022), 103415.

H. Bae, W. Lee. Existence, Gevrey regularity, and decay properties of solutions to Active models in critical spaces. J. Math. Anal. Appl. 506 (2022) 125700.

H. Bae. On the local and global existence of the Hall equations with fractional Laplacian and related equations. Netw. Heterog. Media (2022),645-663.

H. Bae, K. Kang. Local and Global existence of solutions of a Keller-Segel model coupled to the incompressible fluid equations, J. Differential Equations 333 (2022), 407-435.

H. Bae. Global existence of unique solutions to equations for pattern formation in active mixtures. Chaos Solitons Fractals 161, (2022), Paper No. 112337. 6 pp.

H. Bae, W. Lee, J. Shin. Global existence and decay rates of solutions to the viscous water-waves system. Nonlinear Anal. (2022), Paper No. 113062.

H. Bae, J. Shin, On the local and global existence of unique solutions to the L\"ust model. Appl. Math. Lett. 13 (2023), Paper No. 108483.

H. Bae, K. Kang. On the local and global existence, asymptotic behaviors, and decay rates of solutions of the 2½ dimensional Hall equations. J. Math. Fluid Mech. 25 (2023), no 2. 30pp.

H. Bae. Global existence of Active model B with the logarithmic Cahn-Hilliard equation in Wiener space. Chaos Solitons Fractals 175, (2023), Paper No. 113922. 4 pp.

H. Bae, Y. Choi, K. Kang. Well-posedness and asymptotic stability of solutions for the incompressible Toner-Tu model. SIAM J. Math. Anal. 57 (2025), no. 1, 637–660.

H. Bae. J. Shin. Global existence and long time behavior of solutions to some Oldroyd type models in hybrid Besov spaces. J. Math. Anal. Appl. 550 (2025), no. 2, Paper No. 129547, 42 pp.

H. Bae. On the local well-posedness of the equations related to the $2\frac{1}{2}$ dimensional L\"ust model. J. Angew. Math. Mech. 105 (2025), no. 6, Paper No. e70136.

H Bae, K. Kang, J. Shin. On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations. Nonlinearity 38 (2025), no 8. Paper No. 085002

H. Bae, H. Kwon, J. Shin. Global Solutions to Stokes-Magneto equations with Fractional Laplacian. Partial Differ. Equ. Appl. 6 (2025), no.4, Paper No. 32.

H. Bae MCL Filho, A. Mazzucato, HJN Lopes. Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations. Accepted to Pure and Applied Functional Analysis. (dedicated to Professor Peter Constantin on the occasion of his 75-th Birthday).

H. Bae. The global existence of a unique weak solution of Active Model H in viscoelastic fluid. Accepted to Pure and Applied Functional Analysis. (dedicated to Professor Eitan Tadmor on the occasion of his 70-th Birthday).

H. Bae, J. Jung, J.Shin. On the temporal estimates for the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. Accepted to JMFM.

Preprints

H. Bae, K. Kang. J. Shin. On the double Beltrami states in Hall Magnetohydrodynamics.

H. Bae, H. Choi. Existence of solutions and Blow-up conditions of two dimensional models related to the $2\frac{1}{2}$ dimensional L\"ust model.

H. Bae, H. Choi. On temporal decay rates for some dissipative equations with initial data in negative Sobolev spaces.

H. Bae, H. Choi, D. Kim. Stabilization in a Keller-Segel System with Gradient-dependent Damping.

H. Bae, H. Choi, D. Kim. Global bondedness and stabilization in a Keller-Segel model with gradient-dependent source and general indirect signal production.

H. Bae, K. Kang, J. Kelliher, W. Lee. On a genralized incompressible model in two dimensions.