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A sharp bilinear restriction estimate for the sphere and its application to the wave-Schrödinger system. (English) Zbl 1142.35347
Kozono, Hideo (ed.) et al., Asymptotic analysis and singularities. Hyperbolic and dispersive PDEs and fluid mechanics. Papers of the 14th International Research Institute of the Mathematical Society of Japan (MSJ), Sendai, Japan, July, 18–27, 2005. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-40-2/hbk). Advanced Studies in Pure Mathematics 47-1, 65-85 (2006).
Summary: We consider \(2\times 2\to q\) type bilinear restriction estimates for transverse subsets of the sphere, for all \(q> {n+2\over n}\). Moreover, we give its application to the wave-Schrödinger system.
For the entire collection see [Zbl 1130.35003].
35B45 A priori estimates in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
35Q55 NLS equations (nonlinear Schrödinger equations)