The linear profile decomposition for a family of 4th order Schr {o}dinger equations
主 题: The linear profile decomposition for a family of 4th order Schr {o}dinger equations
报告人: 邵双林 (Department of Mathematics, University of Kansas)
时 间: 2014-06-17 10:00-11:00
地 点: 理1569（主持人：章志飞）
In this talk I will talk about the linear profile decomposition for the 4th order Schr\"{o}dinger equations in high dimensions. It is mainly motivated by the recent progress in critical dispersive partial differential equations. The linear profile decomposition says that, after passing to a sub-sequence, an L^2 bounded sequence of initial data may be decomposed as a sum of asymptotically orthogonal pieces that are compact modulo symmetries, plus an error term with arbitrarily small dispersion. The asymptotically orthogonal pieces carry the profile information, which, roughly speaking, describes the location, length, width and oscillation of functions. We use it to prove a dichotomy result on existence of extremal functions to the linear Strichartz inequality. In the argument, there are two key ingredients, the refined Strichartz inequality for the 4th order Schr\"{o}dinger equation, and the concentration-compactness argument. It is a joint work with J. Jiang and B. Stovall.
