Bilinear eigenfunction estimates and the nonlinear Schrodinger equation on surfaces

• 成果类型: Article
• 署名作者: Burq, N; Gérard, P; Tzvetkov, N
• 署名单位: Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0388-x
• 发表日期: 2005
• 页码: 187-223
• 关键词: oscillatory integrals; ill-posedness; inequalities; NORM

摘要

We study the cubic non linear Schrodinger equation (NLS) on compact surfaces. On the sphere S-2 and more generally on Zoll surfaces, we prove that, for s > 1/4, NLS is uniformly well-posed in H-s, which is sharp on the sphere. The main ingredient in our proof is a sharp bilinear estimate for Laplace spectral projectors on compact surfaces.