Convolutions of singular measures and applications to the Zakharov system

Details Convolutions of singular measures and applications to the Zakharov system Convolutions of singular measures and applications to the Zakharov system

2010-09-16

arxiv.org/abs/1009.3250v2

J. Funct. Anal. (2011), Vol. 261, No. 2, 478-506

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.jfa.2011.03.015

Uniform L^2-estimates for the convolution of singular measures with respect
to transversal submanifolds are proved in arbitrary space dimension. The
results of Bennett-Bez are used to extend previous work of
Bejenaru-Herr-Tataru. As an application, it is shown that the 3D Zakharov
system is locally well-posed in the full subcritical regime.

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