People

Bae, Hantaek

Natural Science building (108), 301-12
Dept. of Math. Sciences, UNIST
UNIST-gil 50, Ulsan 689-798

Tel: 052-217-2526
Email: hantaek@unist.ac.kr

Employment & Education

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




Research Area

My research is in the area of evolution PDEs in fluid dynamics, biology, plasma physics, and complex fluids. In particular, I am interested in well-posedness and regularity of initial value problems with limited regularity. My research area can be summarized as follows:

  • Fluid equations: Navier-Stokes equation, Euler equation, Quasi-geostrophic equation
  • 1D models of fluid equations
  • Coupled equations: Keller-Segel equation, MHD equation
  • Free boundary problems


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, 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, 2014.
  10. H. Bae, R. Granero, Global existence for some transport equations with nonlocal velocity, Adv. Math. 269 (2015), 197-219.
  11. H. Bae, Existence and Analyticity of Lei-Lin Solution to the Navier-Stokes Equations, Proc. Amer. Math. Soc. 143 (2015), no. 7, 2887–2892.
  12. 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.
  13. H. Bae, M. Cannone, Log-Lipschitz regularity of the Navier Stokes equations, Nonlinear Analysis 135 (2016), 223-235.
  14. 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.
  15. 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.
  16. 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.
  17. H. Bae, R. Granero, O. Lazar, Global existence of weak solutions to dissipative transport equations with nonlocal velocity. Accepted to Nonlinearity.

Submitted papers

  • H. Bae, K. Kang, Blowup conditions and the global well-posedness of chemotaxis-Navier-Stokes equations in dimension three.
  • H. Bae, J. Kelliher, Propagation of striated regularity of velocity for the Euler equations.
  • H. Bae, H-O Bae, Wake estimates of the incompressible Navier-Stokes equations in exterior domains.


Preprints and Papers in preparation

  • H. Bae, A. Biswas, E. Tadmor, Analyticity of the subcritical quasi-geostrophic equations in Energy spaces, Preprint.
  • H. Bae, J. Kelliher, Striated regularity for transport equations, Preprint.
  • H. Bae, E. Tadmor, Regularizing effects in convection-diffusion equations, In Preparation.
  • H. Bae, On the viscous water wave equations without surface tension: modeling and analysis, In Preparation.
  • H. Bae, Analyticity of the inhomogeneous incompressible Navier-Stokes equations, In Preparation