Department of Mathematics,
Graduate School of Science, Kobe University
Division : Analysis
Building B, Room 324

Personal Website

Research Field : Qualitative research on nonlinear dispersive wave equations

Research Summary : I am interested in the partial differential equations that describe wave propagation phenomena: nonlinear dispersive and wave equations. In particular, I study local and global in time well-posedness and scattering results with modern theory from functional analysis, harmonic analysis and geometric tools. This research area is still active in which major questions are completely unsolved.

Primary Publications :
  1. S. Gustafson, H. Takaoka, T-P. Tsai, Stability in H1/2 of the sum of K solitons for the Benjamin-Ono equation, J. Math. Phys., 50 (2009), 013101, 14 pp.
  2. J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation, Invent. Math., 181 (2010), 39-113.
  3. K. Nakanishi, H. Takaoka and Y. Tsutsumi, Local well-posedness in low regularity of the mKdV equation with periodic boundary condition, Discrete Contin. Dyn. Syst., 28 (2010), 1635-1654.
  4. H. Takaoka, A priori estimates and weak solutions for the derivative nonlinear Schrodinger equation on torus below H^{1/2}, J. Differential Equations, 260 (2016), 818-859.
  5. H. Takaoka, Local well-posedness of the nonlinear Schrodinger equations on the sphere for data in modulation spaces, Communications in Partial Differential Equations, 41 (2016), 732-747.