A bilinear oscillatory integral estimate and bilinear refinements to Strichartz estimates on closed manifolds
| Autor: | Zaher Hani |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Transversality
Scale (ratio) Phase (waves) Mathematics::Analysis of PDEs Bilinear interpolation 35A17 Mathematics - Analysis of PDEs bilinear Strichartz estimates semiclassical time scale Classical Analysis and ODEs (math.CA) FOS: Mathematics Oscillatory integral Mathematics Numerical Analysis Applied Mathematics Mathematical analysis nonlinear Schrödinger equation on compact manifolds 58J40 35B45 Nonlinear system 35S30 Mathematics - Classical Analysis and ODEs 42B20 Analysis bilinear oscillatory integrals transversality Analysis of PDEs (math.AP) |
| Zdroj: | Anal. PDE 5, no. 2 (2012), 339-363 |
| DOI: | 10.48550/arxiv.1008.2827 |
| Popis: | We prove a bilinear $L^2(\R^d) \times L^2(\R^d) \to L^2(\R^{d+1})$ estimate for a pair of oscillatory integral operators with different asymptotic parameters and phase functions satisfying a transversality condition. This is then used to prove a bilinear refinement to Strichartz estimates on closed manifolds, similar to that on $\R^d$, but at a relevant semi-classical scale. These estimates will be employed elsewhere to prove global well-posedness below $H^1$ for the cubic nonlinear Schr\"odinger equation on closed surfaces. Comment: 25 pages, Version 2 (revised version incorporating referee's remarks), to appear in Analysis and PDE |
| Databáze: | OpenAIRE |
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