Modified Strichartz estimates with applications to the Cauchy problem for nonlinear Schrödingier equations
报告人：Takeshi Wada
报告地点：地理楼四楼报告厅
报告时间：2016年10月09日星期日 8:30-9:00
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报告摘要：
Pecher proved a modification of Strichartz estimate, which estimates the solution to the Schrödingier equation. As an application, Pecher considered the following nonlinear Schrödingier equation with power type nonlinearity:
(1)
and proved the well-posedness of (1) in the case where p is close to 1 so that the nonlinear term is not so smooth. Unfortunately, Pecher's estimate is not scale-invariant and hence he could not treat the critical case in with s < n/2, namely when p = 1+4/(n−2s). In this talk we aim at improving Pecher's estimate to the scale invariant form and solving (1) in the critical case.
主讲人简介：
Takeshi Wada，日本Shimane University教授。1991年、1994、2001年于Osaka University分别获学士、硕士、博士学位；1994-1997年在Osaka Prefectural College of Technology任讲师，1997-2004年于Osaka University任Research Associate，2004-2014年于Kumamoto University任副教授，2014年至今于Shimane University任教授。主要从事偏微分方程研究，公开发表论文20余篇。
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