Refinements of the 2-dimensional Strichartz estimate on the maximum wave packet

Abstract

The Strichartz estimates for Schrödinger equations can be improved when the data is spread out in either physical or frequency space. In this paper we give refinements of the 2-dimensional homogeneous Strichartz estimate on the maximum size of a single wave packet. Different approaches are used in the proofs, including arithmetic approaches, polynomial partitioning, and the $l^2$ Decoupling Theorem, for different cases. We also give examples to show that the refinements we obtain cannot be further improved when $2 \leq p \leq 4$ and $p = 6$.

21 pages, 1 figure