Differential and Integral Equations

Bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary and cubic NLS

Jin-Cheng Jiang

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Abstract

In this paper, we establish bilinear and gradient bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary. Using these estimates, we can infer the local well-posedness of the cubic nonlinear Schrödinger equation in $H^s$ for every $s>\frac{2}{3}$ on such manifolds.

Article information

Source
Differential Integral Equations, Volume 24, Number 1/2 (2011), 83-108.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019046

Mathematical Reviews number (MathSciNet)
MR2759353

Zentralblatt MATH identifier
1240.35556

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35S50: Paradifferential operators

Citation

Jiang, Jin-Cheng. Bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary and cubic NLS. Differential Integral Equations 24 (2011), no. 1/2, 83--108. https://projecteuclid.org/euclid.die/1356019046


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