Advances in Differential Equations

On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation

I. Moise and R. Rosa

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Abstract

The existence of the global attractor for a weakly damped, forced Korteweg-de Vries equation is derived in higher-order Sobolev spaces. The main result is the regularity of the global attractor, which is proved to be as regular as the forcing term. This result is attained through a nonobvious decomposition of the solutions used to overcome the lack of a suitable regularization of the linear part of the equation with respect to either the initial condition or the nonhomogeneous term.

Article information

Source
Adv. Differential Equations Volume 2, Number 2 (1997), 257-296.

Dates
First available in Project Euclid: 24 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366809216

Mathematical Reviews number (MathSciNet)
MR1424770

Zentralblatt MATH identifier
1023.35525

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions 58F39

Citation

Moise, I.; Rosa, R. On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation. Adv. Differential Equations 2 (1997), no. 2, 257--296. https://projecteuclid.org/euclid.ade/1366809216.


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