Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation

被引：0

作者：

Tataru, D ^{[1
]}

机构：

[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2000年 / 122卷 / 02期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this article is threefold. First, we use the FBI transform to set up a calculus for partial differential operators with nonsmooth coefficients. Next, this calculus allows us to prove Strichartz type estimates for the wave equation with nonsmooth coefficients. Finally, we use these Strichartz estimates to improve the local theory for second order nonlinear hyperbolic equations.

引用

页码：349 / 376

页数：28

共 50 条

[31] Weighted Strichartz estimates for the wave equation in even space dimensions
Kato, J
Ozawa, T
[J]. MATHEMATISCHE ZEITSCHRIFT, 2004, 247 (04) : 747 - 764
[32] Strichartz Estimates for Schrodinger Operators with Square Potential with Time-Dependent Coefficients
Kawamoto, Masaki
[J]. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2023, 31 (04) : 827 - 845
[33] Strichartz Estimates for Schrödinger Operators with Square Potential with Time-Dependent Coefficients
Masaki Kawamoto
[J]. Differential Equations and Dynamical Systems, 2023, 31 : 827 - 845
[34] Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle
Metcalfe, JL
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (12) : 4839 - 4855
[35] Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients
The Anh Bui
Xuan Thinh Duong
[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2018, 18 (03) : 881 - 916
[36] Global Strichartz estimates for the wave equation with time-periodic potentials
Petkov, Vesselin
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (02) : 357 - 376
[37] STRICHARTZ AND LOCALIZED ENERGY ESTIMATES FOR THE WAVE EQUATION IN STRICTLY CONCAVE DOMAINS
Blair, Matthew D.
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (03) : 817 - 861
[38] GENERALIZED STRICHARTZ ESTIMATES ON PERTURBED WAVE EQUATION AND APPLICATIONS ON STRAUSS CONJECTURE
Yu, Xin
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2011, 24 (5-6) : 443 - 468
[39] The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates
Fabian Hornung
[J]. Journal of Evolution Equations, 2018, 18 : 1085 - 1114
[40] STRICHARTZ ESTIMATES AND LOCAL REGULARITY FOR THE ELASTIC WAVE EQUATION WITH SINGULAR POTENTIALS
Kim, Seongyeon
Kwon, Yehyun
Seo, Ihyeok
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (04) : 1897 - 1911

← 1 2 3 4 5 →