Differential and Integral Equations

Low regularity well-posedness for the periodic Kawahara equation

Takamori Kato

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


In this paper, we consider the well-posedness for the Cauchy problem of the Kawahara equation with low regularity data in the periodic case. We obtain the local well-posedness for $s \geq -3/2$ by a variant of the Fourier restriction norm method introduced by Bourgain. Moreover, these local solutions can be extended globally in time for $s \geq -1$ by the I-method. On the other hand, we prove ill-posedness for $s < -3/2$ in some sense. This is a sharp contrast to the results in the case of $\mathbb{R}$, where the critical exponent is equal to $-2$.

Article information

Differential Integral Equations, Volume 25, Number 11/12 (2012), 1011-1036.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]


Kato, Takamori. Low regularity well-posedness for the periodic Kawahara equation. Differential Integral Equations 25 (2012), no. 11/12, 1011--1036. https://projecteuclid.org/euclid.die/1356012249

Export citation