Hokkaido Mathematical Journal

Bilinear Strichartz estimates and applications to the cubic nonlinear Schrödinger equation in two space dimensions

Hideo TAKAOKA

Full-text: Open access

Abstract

The initial value problem for the defocusing cubic nonlinear Schrödinger equation on ${\Bbb R}^2$ is locally well-posed in Hs for s ≥ 0. The L^2-space norm is invariant under rescaling to the equation, then the critical regularity is s = 0. In this note, we prove the global well-posedness in Hs for all s > 1/2. The proof uses the almost conservation approach by adding additional (non-resonant) correction terms to the original almost conserved energy.

Article information

Source
Hokkaido Math. J., Volume 37, Number 4 (2008), 861-870.

Dates
First available in Project Euclid: 31 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1249046373

Digital Object Identifier
doi:10.14492/hokmj/1249046373

Mathematical Reviews number (MathSciNet)
MR2474180

Zentralblatt MATH identifier
1173.35694

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

Keywords
Strichartz estimate nonlinear Schrödinger equation global well-posedness

Citation

TAKAOKA, Hideo. Bilinear Strichartz estimates and applications to the cubic nonlinear Schrödinger equation in two space dimensions. Hokkaido Math. J. 37 (2008), no. 4, 861--870. doi:10.14492/hokmj/1249046373. https://projecteuclid.org/euclid.hokmj/1249046373


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