Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus

Jun ichi Segata

doi:10.1016/j.jde.2012.02.016

Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus

Jun ichi Segata

研究成果: ジャーナルへの寄稿 › 学術誌 › 査読

6 被引用数 (Scopus)

抄録

We consider the time local and global well-posedness for the fourth order nonlinear Schrödinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS).

本文言語	英語
ページ（範囲）	5994-6011
ページ数	18
ジャーナル	Journal of Differential Equations
巻	252
号	11
DOI	https://doi.org/10.1016/j.jde.2012.02.016
出版ステータス	出版済み - 6月 1 2012
外部発表	はい

!!!All Science Journal Classification (ASJC) codes

分析
応用数学

文献へのアクセス

10.1016/j.jde.2012.02.016

他のファイルとリンク

フィンガープリント

「Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{f91f152bac2f4c00affa18bcc507c7a9,

title = "Refined energy inequality with application to well-posedness for the fourth order nonlinear Schr{\"o}dinger type equation on torus",

abstract = "We consider the time local and global well-posedness for the fourth order nonlinear Schr{\"o}dinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS).",

author = "Segata, {Jun ichi}",

note = "Funding Information: The author would like to thank Dr. Masaya Maeda for fruitful comments. The author is partially supported by MEXT, Grant-in-Aid for Young Scientists (B) 21740122.",

year = "2012",

month = jun,

day = "1",

doi = "10.1016/j.jde.2012.02.016",

language = "English",

volume = "252",

pages = "5994--6011",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "11",

}

TY - JOUR

T1 - Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus

AU - Segata, Jun ichi

N1 - Funding Information: The author would like to thank Dr. Masaya Maeda for fruitful comments. The author is partially supported by MEXT, Grant-in-Aid for Young Scientists (B) 21740122.

PY - 2012/6/1

Y1 - 2012/6/1

N2 - We consider the time local and global well-posedness for the fourth order nonlinear Schrödinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS).

AB - We consider the time local and global well-posedness for the fourth order nonlinear Schrödinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS).

UR - http://www.scopus.com/inward/record.url?scp=84859633945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859633945&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2012.02.016

DO - 10.1016/j.jde.2012.02.016

M3 - Article

AN - SCOPUS:84859633945

SN - 0022-0396

VL - 252

SP - 5994

EP - 6011

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -