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
相关论文
共 50 条
  • [11] Probabilistic Radial Strichartz Estimates and Its Application
    Hwang, Gyeongha
    FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2024, 67 (02): : 199 - 216
  • [12] GENERALIZED AND WEIGHTED STRICHARTZ ESTIMATES
    Jiang, Jin-Cheng
    Wang, Chengbo
    Yu, Xin
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (05) : 1723 - 1752
  • [13] Extended Strichartz Estimates for the Heat Equation with a Strichartz Type Potential
    Nikolova, Elena
    Tarulli, Mirko
    Venkov, George
    APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE20), 2021, 2333
  • [14] Strichartz estimates on the quaternion Heisenberg group
    Song, Naiqi
    Zhao, Jiman
    BULLETIN DES SCIENCES MATHEMATIQUES, 2014, 138 (02): : 293 - 315
  • [15] STRICHARTZ ESTIMATES ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS
    Bouclet, Jean-Marc
    ANALYSIS & PDE, 2011, 4 (01): : 1 - 84
  • [16] Strichartz estimates associated with the Grushin operator
    Ghosh, Sunit
    Mondal, Shyam Swarup
    Swain, Jitendriya
    NEW YORK JOURNAL OF MATHEMATICS, 2024, 30 : 1621 - 1642
  • [17] A refinement of the Strichartz inequality for the wave equation with applications
    Ramos, Javier
    ADVANCES IN MATHEMATICS, 2012, 230 (02) : 649 - 698
  • [18] Strichartz estimates for equations with structured Lipschitz coefficients
    Frey, Dorothee
    Schippa, Robert
    JOURNAL OF EVOLUTION EQUATIONS, 2023, 23 (03)
  • [19] On the boundary Strichartz estimates for wave and Schrodinger equations
    Guo, Zihua
    Li, Ji
    Nakanishi, Kenji
    Yan, Lixin
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (11) : 5656 - 5675
  • [20] Strichartz Estimates on Schwarzschild Black Hole Backgrounds
    Marzuola, Jeremy
    Metcalfe, Jason
    Tataru, Daniel
    Tohaneanu, Mihai
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 293 (01) : 37 - 83
12345