Refinements of Strichartz estimates on tori and applications

被引：0
|
作者：
Schippa, Robert [1 ]
机构：
[1] Univ Calif Berkeley, Dept Math, 1067 Evans Hall, Berkeley, CA 94720 USA
来源：
MATHEMATISCHE ANNALEN | 2025年 / 391卷 / 03期
关键词：
42B37; 35B45; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; MODIFIED KDV; MKDV; INEQUALITIES; PROOF;
D O I：
10.1007/s00208-024-03001-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show trilinear Strichartz estimates in one and two dimensions on frequency-dependent time intervals. These improve on the corresponding linear estimates of periodic solutions to the Schr & ouml;dinger equation. The proof combines decoupling iterations with bilinear short-time Strichartz estimates. Secondly, we use decoupling to show new linear Strichartz estimates on frequency dependent time intervals. We apply these in case of the Airy propagator to obtain the sharp Sobolev regularity for the existence of solutions to the modified Korteweg-de Vries equation.
引用
收藏
页码：3245 / 3294
页数：50
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