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^*

^*此作品的通讯作者

China Academy of Engineering Physics

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	635-644
页数	10
期刊	Journal of Mathematical Analysis and Applications
卷	369
期	2
DOI	https://doi.org/10.1016/j.jmaa.2010.04.003
出版状态	已出版 - 9月 2010
已对外发布	是

访问文件

10.1016/j.jmaa.2010.04.003

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{27a3b3e48bc1423db910faf0b6492865,

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.",

keywords = "Fourth-order wave equation, Global well-posedness, Low regularity, Strichartz-type estimate",

author = "Junyong Zhang",

year = "2010",

month = sep,

doi = "10.1016/j.jmaa.2010.04.003",

language = "English",

volume = "369",

pages = "635--644",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Global existence for rough solutions of a fourth-order nonlinear wave equation

AU - Zhang, Junyong

PY - 2010/9

Y1 - 2010/9

N2 - 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.

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

U2 - 10.1016/j.jmaa.2010.04.003

DO - 10.1016/j.jmaa.2010.04.003

M3 - Article

AN - SCOPUS:77953024486

SN - 0022-247X

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

摘要

访问文件

其它文件与链接

学术指纹

引用此