Linear profile decompositions for a family of fourth order Schr\"odinger equations
Analysis of PDEs
2017-04-19 v2 Classical Analysis and ODEs
Abstract
We establish linear profile decompositions for the fourth order Schr\"odinger equation and for certain fourth order perturbations of the Schr\"odinger equation, in dimensions greater than or equal to two. We apply these results to prove dichotomy results on the existence of extremizers for the associated Stein--Tomas/Strichartz inequalities; along the way, we also obtain lower bounds for the norms of these operators.
Keywords
Cite
@article{arxiv.1410.7520,
title = {Linear profile decompositions for a family of fourth order Schr\"odinger equations},
author = {Jincheng Jiang and Shuanglin Shao and Betsy Stovall},
journal= {arXiv preprint arXiv:1410.7520},
year = {2017}
}
Comments
25 pages. The proof of the old Theorem 7 is clarified and references updated