Differential and Integral Equations

Growth of the $H^s$-norm for the modified KdV equation

Germán E. Fonseca

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We study the growth of the $H^s$-norm for solutions of the modified Korteweg-de Vries equation, corresponding to data in $H^s$ for noninteger values of $s$ in the case where global solutions exist. The presence of conservation laws and the local existence theory permit us to obtain upper "polynomial" bounds, for the $H^s$-norm of these solutions, with power depending on the distance to the closest integer to $s$.

Article information

Differential Integral Equations, Volume 13, Number 7-9 (2000), 1081-1093.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35A05 35B45: A priori estimates


Fonseca, Germán E. Growth of the $H^s$-norm for the modified KdV equation. Differential Integral Equations 13 (2000), no. 7-9, 1081--1093. https://projecteuclid.org/euclid.die/1356061211

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