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2021 Global existence of small solutions for a quadratic nonlinear fourth-order Schrödinger equation in six space dimensions
Kazuki Aoki
Tohoku Math. J. (2) 73(1): 49-98 (2021). DOI: 10.2748/tmj.20191217

Abstract

We consider the Cauchy problem for the nonlinear fourth-order Schrödinger equation in six space dimensions with a quadratic nonlinearity. We prove a global existence and time decay estimates of solutions if the data are small, regular and decay rapidly at infinity.

Citation

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Kazuki Aoki. "Global existence of small solutions for a quadratic nonlinear fourth-order Schrödinger equation in six space dimensions." Tohoku Math. J. (2) 73 (1) 49 - 98, 2021. https://doi.org/10.2748/tmj.20191217

Information

Published: 2021
First available in Project Euclid: 22 March 2021

Digital Object Identifier: 10.2748/tmj.20191217

Subjects:
Primary: 35Q55

Keywords: fourth-order nonlinear Schrödinger equation , global existence , the normal form method

Rights: Copyright © 2021 Tohoku University

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Vol.73 • No. 1 • 2021
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