STRICHARTZ ESTIMATES IN SIMILARITY COORDINATES AND STABLE BLOWUP FOR THE CRITICAL WAVE EQUATION

被引：21

作者：

Donninger, Roland ^{[1
,2
]}

机构：

[1] Rhein Friedrich Wilhelms Univ Bonn, Math Inst, Bonn, Germany

[2] Univ Vienna, Fak Math, Vienna, Austria

来源：

DUKE MATHEMATICAL JOURNAL | 2017年 / 166卷 / 09期

关键词：

ENERGY-CRITICAL WAVE; SELF-SIMILAR BLOWUP; UP SOLUTIONS; CHARACTERISTIC POINTS; DISPERSIVE EQUATIONS; RADIAL SOLUTIONS; GLOBAL DYNAMICS; GROUND-STATE; EXISTENCE; SCATTERING;

D O I：

10.1215/00127094-0000009X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a (time-dependent) self-similar potential. As an application, we consider the critical wave equation and prove the asymptotic stability of the ordinary differential equations blowup profile in the energy space.

引用

页码：1627 / 1683

页数：57

共 50 条

[31] Strichartz estimates and maximal operators for the wave equation in R3
Beceanu, Marius
Goldberg, Michael
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (03) : 1476 - 1510
[32] Nonscattering solutions and blowup at infinity for the critical wave equation
Donninger, Roland
Krieger, Joachim
MATHEMATISCHE ANNALEN, 2013, 357 (01) : 89 - 163
[33] Blowup stability at optimal regularity for the critical wave equation
Donninger, Roland
Rao, Ziping
ADVANCES IN MATHEMATICS, 2020, 370
[34] Global Strichartz estimates for the wave equation with time-periodic potentials
Petkov, Vesselin
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 235 (02) : 357 - 376
[35] Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds
Zhang, Junyong
ADVANCES IN MATHEMATICS, 2015, 271 : 91 - 111
[36] STRICHARTZ AND LOCALIZED ENERGY ESTIMATES FOR THE WAVE EQUATION IN STRICTLY CONCAVE DOMAINS
Blair, Matthew D.
AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (03) : 817 - 861
[37] GENERALIZED STRICHARTZ ESTIMATES ON PERTURBED WAVE EQUATION AND APPLICATIONS ON STRAUSS CONJECTURE
Yu, Xin
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2011, 24 (5-6) : 443 - 468
[38] Nonscattering solutions and blowup at infinity for the critical wave equation
Roland Donninger
Joachim Krieger
Mathematische Annalen, 2013, 357 : 89 - 163
[39] STRICHARTZ ESTIMATES AND LOCAL REGULARITY FOR THE ELASTIC WAVE EQUATION WITH SINGULAR POTENTIALS
Kim, Seongyeon
Kwon, Yehyun
Seo, Ihyeok
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (04) : 1897 - 1911
[40] Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
Tataru, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 353 (02) : 795 - 807

← 1 2 3 4 5 →