Global existence for rough solutions of a fourth-order nonlinear wave equation

Junyong Zhang

doi:10.1016/j.jmaa.2010.04.003

Global existence for rough solutions of a fourth-order nonlinear wave equation

Junyong Zhang^*

^*Corresponding author for this work

China Academy of Engineering Physics

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

5 Citations (Scopus)

Abstract

In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in H^s(Rⁿ) for s > min {n-2/2,n/4} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.

Original language	English
Pages (from-to)	635-644
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	369
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.04.003
Publication status	Published - Sept 2010
Externally published	Yes

Keywords

Fourth-order wave equation
Global well-posedness
Low regularity
Strichartz-type estimate

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10.1016/j.jmaa.2010.04.003

Cite this

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title = "Global existence for rough solutions of a fourth-order nonlinear wave equation",

abstract = "In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in Hs(Rn) for s > min \{n-2/2,n/4\} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.",

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AB - In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in Hs(Rn) for s > min {n-2/2,n/4} by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.

KW - Fourth-order wave equation

KW - Global well-posedness

KW - Low regularity

KW - Strichartz-type estimate

UR - https://www.scopus.com/pages/publications/77953024486

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DO - 10.1016/j.jmaa.2010.04.003

M3 - Article

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VL - 369

SP - 635

EP - 644

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Global existence for rough solutions of a fourth-order nonlinear wave equation

Abstract

Keywords

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