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.

Preprints

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

• 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. The global existence of a unique weak solution of Active Model H in viscoelastic fluid.

• H. Bae  MCL Filho, A. Mazzucato, HJN Lopes. Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations