偏微分方程式セミナー: Remarks on $L^2$-decay of small solutions to derivative nonlinear Schrodinger equations with weakly dissipative structure, 砂川 秀明 氏

Time：16:30-17:30

Place：理学部3号館3-309室 (hybrid)

Organizer：黒田 紘敏、浜向 直

Speaker：砂川 秀明 氏 (大阪公立大学)

Title：Remarks on $L^2$-decay of small solutions to derivative nonlinear Schrodinger equations with weakly dissipative structure

Abstract：Consider the initial value problem for the cubic derivative nonlinear Schrodinger equations in one space dimension with small initial data. Under the weak dissipativity condition in the sense of Li-NIshii-Sagawa-Sunagawa(2021), the global solution decays like $(\log t)^{-1/4}$ in $L^2$, and this rate is best possible in general.
In this talk, I will show that this decay rate is slightly lowered if the Fourier transform of the initial data vanishes at the point where the dissipation is not effective. Several remarks related to this result will be also given.
This talk is based on a joint work with Chunhua Li, Yuji Sagawa and Shinpei Washio.