Speaker: Professor Yoshio Tsutsumi (Kyoto University)
Title:  Local well-posedness in low regularity of the mKdV equation
with periodic boundary condition
Abstract: I talk about the local well-posedness in low regularity of
the Cauchy prob- lem for the mKdV equation on one-dimensional torus by
modifying the Fourier restriction method due to Bourgain. It seems
interesting and important to study the well-posedness in low
regularity for the mKdV equation. Because the mKdV equation is
prototype among nonlinear dispersive equations and if we consider the
equation in low regular spaces, it would reveal specific features of
nonlinear interaction, which might be hidden behind the high
regularity. I present a brief survey on the recent results on the
well-posedness in low regularity and explain our results, which has
recently been obtained in collaboration with Kenji Nakanishi and Hideo
Takaoka. In our proof, we modify the Fourier restriction norm to take
into account the oscillation of the phase of solution, which is caused
by the nonlinear interaction.
Time:14:10~15:10, May. 3(Mon.), 2010
Place:Room 101, New Mathematics Building, National Taiwan University(臺灣大學新數館101室)