Differential and Integral Equations

The Cauchy problem for the semilinear quintic Schrödinger equation in one dimension

Nikolaos Tzirakis

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


We show that the Cauchy problem for the quintic NLS on $\mathbf{R}$ is globally well posed in $H^s$ for $4/9<s\leq 1/2$. Since we work below the energy space we cannot immediately use the energy. Instead we use the "I-method" introduced by J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao. This method allows us to define a modification of the energy functional that is "almost conserved" and thus can be used to iterate the local result.

Article information

Differential Integral Equations, Volume 18, Number 8 (2005), 947-960.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]


Tzirakis, Nikolaos. The Cauchy problem for the semilinear quintic Schrödinger equation in one dimension. Differential Integral Equations 18 (2005), no. 8, 947--960. https://projecteuclid.org/euclid.die/1356060152

Export citation