## Differential and Integral Equations

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

Germán E. Fonseca

#### Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356061211

Mathematical Reviews number (MathSciNet)
MR1775247

Zentralblatt MATH identifier
0976.35065

Subjects
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