The proof of the refined Strichartz inequality for the 4th Schr {o}dinger operator
主 题: The proof of the refined Strichartz inequality for the 4th Schr {o}dinger operator
报告人: 邵双林 (Department of Mathematics, University of Kansas)
时 间: 2014-06-18 15:30-16:30
地 点: 理1493（主持人：章志飞）
In dispersive PDE, it is well known that the Strichartz inequality describes decay of solutions in space and plays an important role in the Cauchy theory. In this talk we will talk about the proof of the refined Strichartz inequality. Our inequality is improved in the sense that, to control a norm, only partial information of functions is needed; for example, only the part of functions supported on an annulus, and even on a small cube. In the proof, the difficulty is that the hyper-surface associated with the 4th order Schr\"{o}dinger operator has vanishing Gaussian curvature at the origin. The novelty is the idea of localization, which reduces the estimate to Tao's bilinear Fourier restriction theorem for bounded elliptic surfaces. It is a joint work with J. Jiang and B. Stovall.
