Strichartz estimates and strauss conjecture on non-trapping asymptotically hyperbolic manifolds

YANNICK SIRE; CHRISTOPHER D. SOGGE; CHENGBO WANG; JUNYONG ZHANG

doi:10.1090/TRAN/8210

Strichartz estimates and strauss conjecture on non-trapping asymptotically hyperbolic manifolds

YANNICK SIRE, CHRISTOPHER D. SOGGE, CHENGBO WANG, JUNYONG ZHANG

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from [Ann. Inst. Fourier, Grenoble 68 (2018), pp. 1011-1075] and arguments borrowed from [Analysis PDE 9 (2016), pp. 151-192], [Adv. Math. 271 (2015), pp. 91-111]. As an application, we prove the small data global existence for any power p ∈(1,1 + 4 n-1) for the shifted wave equation in this setting, involving nonlinearities of the form ±|u|p or ±|u|p-1u, which answers partially an open question raised in [Discrete Contin. Dyn. Syst. 39 (2019), pp. 7081-7099].

Original language	English
Pages (from-to)	7639-7668
Number of pages	30
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	11
DOIs	https://doi.org/10.1090/TRAN/8210
Publication status	Published - 2020

Keywords

Asymptotically hyperbolic manifold
Shifted wave
Spectral measure
Strauss conjecture
Strichartz estimate

Access to Document

10.1090/TRAN/8210

Cite this

@article{2a1e5d713a794b3cbcd4bf17a23ce6d5,

title = "Strichartz estimates and strauss conjecture on non-trapping asymptotically hyperbolic manifolds",

abstract = "We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from [Ann. Inst. Fourier, Grenoble 68 (2018), pp. 1011-1075] and arguments borrowed from [Analysis PDE 9 (2016), pp. 151-192], [Adv. Math. 271 (2015), pp. 91-111]. As an application, we prove the small data global existence for any power p ∈(1,1 + 4 n-1) for the shifted wave equation in this setting, involving nonlinearities of the form ±|u|p or ±|u|p-1u, which answers partially an open question raised in [Discrete Contin. Dyn. Syst. 39 (2019), pp. 7081-7099].",

keywords = "Asymptotically hyperbolic manifold, Shifted wave, Spectral measure, Strauss conjecture, Strichartz estimate",

author = "YANNICK SIRE and SOGGE, {CHRISTOPHER D.} and CHENGBO WANG and JUNYONG ZHANG",

note = "Publisher Copyright: {\textcopyright} 2020 American Mathematical Society.",

year = "2020",

doi = "10.1090/TRAN/8210",

language = "English",

volume = "373",

pages = "7639--7668",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - Strichartz estimates and strauss conjecture on non-trapping asymptotically hyperbolic manifolds

AU - SIRE, YANNICK

AU - SOGGE, CHRISTOPHER D.

AU - WANG, CHENGBO

AU - ZHANG, JUNYONG

PY - 2020

Y1 - 2020

N2 - We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from [Ann. Inst. Fourier, Grenoble 68 (2018), pp. 1011-1075] and arguments borrowed from [Analysis PDE 9 (2016), pp. 151-192], [Adv. Math. 271 (2015), pp. 91-111]. As an application, we prove the small data global existence for any power p ∈(1,1 + 4 n-1) for the shifted wave equation in this setting, involving nonlinearities of the form ±|u|p or ±|u|p-1u, which answers partially an open question raised in [Discrete Contin. Dyn. Syst. 39 (2019), pp. 7081-7099].

AB - We prove global-in-time Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds. The key tools are the spectral measure estimates from [Ann. Inst. Fourier, Grenoble 68 (2018), pp. 1011-1075] and arguments borrowed from [Analysis PDE 9 (2016), pp. 151-192], [Adv. Math. 271 (2015), pp. 91-111]. As an application, we prove the small data global existence for any power p ∈(1,1 + 4 n-1) for the shifted wave equation in this setting, involving nonlinearities of the form ±|u|p or ±|u|p-1u, which answers partially an open question raised in [Discrete Contin. Dyn. Syst. 39 (2019), pp. 7081-7099].

KW - Asymptotically hyperbolic manifold

KW - Shifted wave

KW - Spectral measure

KW - Strauss conjecture

KW - Strichartz estimate

UR - http://www.scopus.com/inward/record.url?scp=85094867611&partnerID=8YFLogxK

U2 - 10.1090/TRAN/8210

DO - 10.1090/TRAN/8210

M3 - Article

AN - SCOPUS:85094867611

SN - 0002-9947

VL - 373

SP - 7639

EP - 7668

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -

Strichartz estimates and strauss conjecture on non-trapping asymptotically hyperbolic manifolds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this