## Hokkaido Mathematical Journal

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

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

#### 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