Translator Disclaimer
March/April 2016 Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces
Tomoya Kato
Adv. Differential Equations 21(3/4): 201-234 (March/April 2016).

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.

Citation

Download Citation

Tomoya Kato. "Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces." Adv. Differential Equations 21 (3/4) 201 - 234, March/April 2016.

Information

Published: March/April 2016
First available in Project Euclid: 18 February 2016

zbMATH: 1375.35493
MathSciNet: MR3461293

Subjects:
Primary: 35G05 , 35G25 , 35Q55

Rights: Copyright © 2016 Khayyam Publishing, Inc.

JOURNAL ARTICLE
34 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.21 • No. 3/4 • March/April 2016
Back to Top