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

  • 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, 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.
  • H. Bae, R. Granero, 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.

Submitted papers

  • H. Bae, K. Kang, Blowup conditions and the global well-posedness of chemotaxis-Navier-Stokes equations in dimension three.
  • H. Bae, R. Granero, O. Lazar, Global existence of weak solutions to dissipative transport equations with nonlocal velocity.
  • H. Bae, J. Kelliher, Propagation of striated regularity of velocity for the Euler equations.

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.