Advances in Differential Equations

Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces

Tomoya Kato

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Abstract

In this paper, we consider the Cauchy problem for the nonlinear higher order Schrödinger equations on modulation spaces $M_{p,q}^s$ and show the existence of a unique global solution by using integrability of time decay factors of time decay estimates. As a result, we are able to deal with wider classes of a nonlinearity and a solution space. Moreover, we study time decay estimates of a semi--group $e^{it\phi(\sqrt{-\Delta})}$ with a polynomial symbol $\phi$. Considering multiplicities of critical points and inflection points of $\phi$ carefully, we have time decay estimates with better time decay rate.

Article information

Source
Adv. Differential Equations Volume 21, Number 3/4 (2016), 201-234.

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1455805257

Mathematical Reviews number (MathSciNet)
MR3461293

Subjects
Primary: 35G25: Initial value problems for nonlinear higher-order equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35G05: Linear higher-order equations

Citation

Kato, Tomoya. Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces. Adv. Differential Equations 21 (2016), no. 3/4, 201--234. https://projecteuclid.org/euclid.ade/1455805257.


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