Hideo TAKAOKA 
Hideo TAKAOKA
Department of Mathematics,
Graduate School of Science, Kobe University 
Division : Analysis
Professor 
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 wellposedness 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 : 

S. Gustafson, H. Takaoka, TP. Tsai, Stability in H^{1/2} of the sum of K solitons for the BenjaminOno equation, J. Math. Phys., 50 (2009), 013101, 14 pp.

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), 39113.

K. Nakanishi, H. Takaoka and Y. Tsutsumi, Local wellposedness in low regularity of the mKdV equation with periodic boundary condition, Discrete Contin. Dyn. Syst., 28 (2010), 16351654.

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), 818859.

H. Takaoka, Local wellposedness of the nonlinear Schrodinger equations on the sphere for data in modulation spaces, Communications in Partial Differential Equations, 41 (2016), 732747.


