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

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3 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 languageEnglish
Pages (from-to)5994-6011
Number of pages18
JournalJournal of Differential Equations
Volume252
Issue number11
DOIs
Publication statusPublished - Jun 1 2012
Externally publishedYes

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Energy Inequality
Well-posedness
Fourth Order
Torus
Derivatives
Global Well-posedness
Local Time
Energy Method
A Priori Estimates
Derivative
Unknown
Term
Energy

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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).",
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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).

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