Bulletin of the Belgian Mathematical Society - Simon Stevin

On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation

Van Duong Dinh

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Abstract

We prove the local well-posedness for the nonlinear fourth-order Schrödinger equation (NL4S) in Sobolev spaces. We also study the regularity of local solutions in the sub-critical case. A direct consequence of this regularity is the global well-posedness above mass and energy spaces under some assumptions. Finally, we show the ill-posedness for (NL4S) in some cases of the super-critical range.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 415-437.

Dates
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631236

Mathematical Reviews number (MathSciNet)
MR3852677

Zentralblatt MATH identifier
06970023

Subjects
Primary: 35G20: Nonlinear higher-order equations 35G25: Initial value problems for nonlinear higher-order equations

Keywords
Nonlinear fourth-order Schrödinger Local well-posedness Regularity Ill-posedness

Citation

Dinh, Van Duong. On well-posedness, regularity and ill-posedness for the nonlinear fourth-order Schrödinger equation. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 415--437. https://projecteuclid.org/euclid.bbms/1536631236


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