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

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 intr...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 252; no. 11; pp. 5994 - 6011
Main Author Segata, Jun-ichi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2012
Subjects
Nonlinear Schrödinger type equation
Well-posedness on torus
secondary
Well-posedness on torus
Nonlinear Schrödinger type equation
primary
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Summary: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).
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.02.016