# People

## Employment & Education

• Associate Professor, Department of Mathematical Sciences, UNIST (2018/09 -)
• Assistant Professor, Department of Mathematical Sciences, UNIST (2014/08 - 2018/08)
• Krener Assistant Professor, Department of Mathematics, UC Davis (2012/07 – 2014/07)
• Research Associate, Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland (2009/08 – 2012/06)
• Courant Institute of Mathematical Sciences, New York University, Ph.D. (2004/09 - 2009/05)
• Seoul National University, B.S. (1998/03 - 2004/08)

## 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

1. H. Bae. Global well-posedness of the dissipative quasi-geostrophic equations in critical spaces, Proc. Amer. Math. Soc. 136 (2008), 257-261.
2. H. Bae. Solvability of the free boundary problem of the Navier-Stokes equations with surface tension, Discrete Contin. Dyn. Syst. 29 (2011), 769-801.
3. H. Bae. Global well-posedness for the critical quasi-geostrophic equations in L^{\infty}, Nonlinear Anal. 75 (2011), 1995-2002.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. H. Bae, R. Granero-Belinchon. Global existence for some transport equations with nonlocal velocity, Adv. Math. 269 (2015), 197-219.
10. H. Bae. Existence and Analyticity of Lei-Lin Solution to the Navier-Stokes Equations, Proc. Amer. Math. Soc. 143 (2015), no. 7, 2887–2892.
11. 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.
12. H. Bae, M. Cannone. Log-Lipschitz regularity of the Navier Stokes equations, Nonlinear Analysis 135 (2016), 223-235.
13. 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.
14. 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.
15. 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.
16. H. Bae, R. Granero-Belinchon, O. Lazar. Global existence of weak solutions to dissipative transport equations with nonlocal velocity. Nonlinearity 31 (2018) 1484-1515.
17. H. Bae. Analyticity of the inhomogeneous incompressible Navier-Stokes equations. Appl. Math. Lett. 83 (2018), 200–206.
18. 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.
19. 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.
20. H. Bae, W. Lee, J. Shin. A blow-up criterion for the inhomogeneous incompressible Euler equations. Nonlinear Anal. 196 (2020), 111774
21. H. Bae. Analyticity of solutions to the barotropic compressible Navier-Stokes Equations. Journal of Differential Equations 269 (2020) 1718-1743.
22. H. Bae, R. Granero-Belinchon. Global existence and exponential decay to equilibrium for DLSS-type equations. Journal of Dynamics and Differential Equations (2020).
23. H. Bae. Global existence of solutions to some equations modeling phase separation of self-propelled particles. SN Partial Differ. Equ. Appl. 1, 47 (2020).
24. 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.
25. 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).
26. 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.
27. 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.
28. 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.
29. H. Bae, R. Granero-Belinchon. Singularity formation for the Serre-Green-Naghdi equations and applications to abcd-Boussinesq systems. Accepted to Monatshefte für Mathematik.
30. H. Bae, K. Kang. Local and Global existence of solutions of a Keller-Segel model coupled to the incompressible fluid equations, Submitted.
31. H. Bae, W. Lee, J. Shin. Global existence and decay rates of solutions to the viscous water-waves system. Submitted.
32. H. Bae, K. Kang. On the local and global existence, asymptotic behaviors, and decay rates of solutions of the $2\frac{1}{2}$ dimensional Hall equations. Submitted.
33. H. Bae, J. Shin. Weak-strong uniqueness for the incompressible Navier-Stokes equations in Fourier-Besov spaces. Submitted.
34. H. Bae. On the local and global existence of the Hall equations with fractional Laplacian and related equations. Submitted

## Conference Proceedings

1. H. Bae, K. Trivisa. On the Doi model for the suspensions of rod-like molecules in compressible fluids. Hyperbolic problems: theory, numerics, applications, 285–292, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), 2014.