Translator Disclaimer
July 2010 Analyticity and smoothing effect for the fifth order KdV type equation
Kyoko Tomoeda
Proc. Japan Acad. Ser. A Math. Sci. 86(7): 101-106 (July 2010). DOI: 10.3792/pjaa.86.101

Abstract

We consider the initial value problem for the reduced fifth order KdV type equation: $\partial_{t}u-\partial_{x}^{5}u-10\partial_{x}(u^{3})+5\partial_{x}(\partial_{x}u)^{2}=0$ which is obtained by removing the nonlinear term $10\partial_{x}(u\partial_{x}^{2} u)$ from the fifth order KdV equation. We show the existence of the local solution which is real analytic in both time and space variables, if the initial data $\phi\in H^{s}(\mathbf{R})$ $(s>1/8)$ satisfies the condition \begin{equation*} ∑_{k=0}^{∞}\frac{A_{0}^{k}}{k!}{\|}(x\partial_{x})^{k}φ{\|}_{H^{s}}<{∞}, \end{equation*} for some constant $A_{0}(0<A_{0}<1)$. Moreover, the smoothing effect for this equation is obtained. The proof of our main result is based on the argument used in [5].

Citation

Download Citation

Kyoko Tomoeda. "Analyticity and smoothing effect for the fifth order KdV type equation." Proc. Japan Acad. Ser. A Math. Sci. 86 (7) 101 - 106, July 2010. https://doi.org/10.3792/pjaa.86.101

Information

Published: July 2010
First available in Project Euclid: 21 July 2010

zbMATH: 1205.35276
MathSciNet: MR2663650
Digital Object Identifier: 10.3792/pjaa.86.101

Subjects:
Primary: 35Q53

Rights: Copyright © 2010 The Japan Academy

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.86 • No. 7 • July 2010
Back to Top