Anisotropic bilinear $L^2$ estimates related to the 3d wave equation

Details Anisotropic bilinear $L^2$ estimates related to the 3d wave equation Anisotropic bilinear $L^2$ estimates related to the 3d wave equation

2008-04-27

arxiv.org/abs/0804.4302v1

Mathematics

Analysis of PDEs

41 pages, 1 figure

Scientific paper

We first review the $L^2$ bilinear generalizations of the $L^4$ estimate of Strichartz for solutions of the homogeneous 3D wave equation, and give a short proof based solely on an estimate for the volume of intersection of two thickened spheres. We then go on to prove a number of new results, the main theme being how additional, anisotropic Fourier restrictions influence the estimates. Moreover, we prove some refinements which are able to simultaneously detect both concentrations and nonconcentrations in Fourier space.

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