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

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

6 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	5994-6011
Number of pages	18
Journal	Journal of Differential Equations
Volume	252
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2012.02.016
Publication status	Published - Jun 1 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Access to Document

10.1016/j.jde.2012.02.016

Cite this

@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 -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this