Open Access
Translator Disclaimer
2007 On the well-posedness of the Cauchy problem for dissipative modified Korteweg-de Vries equations
Wengu Chen, Junfeng Li, Changxing Miao
Differential Integral Equations 20(11): 1285-1301 (2007).

Abstract

In this paper we consider some dissipative versions of the modified Korteweg--de~Vries equation $u_t+u_{xxx}+|D_x|^{\alpha}u+u^2u_x=0$ with $0 <\alpha\leq 3$. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces $H^s({ \mathbb R})$ for $s>1/4-\alpha/4$ on the basis of the $[k;\,Z]-$multiplier norm estimate obtained by Tao in [11] for KdV equation.

Citation

Download Citation

Wengu Chen. Junfeng Li. Changxing Miao. "On the well-posedness of the Cauchy problem for dissipative modified Korteweg-de Vries equations." Differential Integral Equations 20 (11) 1285 - 1301, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35407
MathSciNet: MR2372427

Subjects:
Primary: 35Q53
Secondary: 35B30

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.20 • No. 11 • 2007
Back to Top