Differential and Integral Equations

On the well-posedness of the Cauchy problem for dissipative modified Korteweg-de Vries equations

Wengu Chen, Junfeng Li, and Changxing Miao

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations Volume 20, Number 11 (2007), 1285-1301.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039289

Mathematical Reviews number (MathSciNet)
MR2372427

Zentralblatt MATH identifier
1212.35407

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Chen, Wengu; Miao, Changxing; Li, Junfeng. On the well-posedness of the Cauchy problem for dissipative modified Korteweg-de Vries equations. Differential Integral Equations 20 (2007), no. 11, 1285--1301. https://projecteuclid.org/euclid.die/1356039289.


Export citation