Convolutions of singular measures and applications to the Zakharov system
arXiv:1009.3250 · doi:10.1016/j.jfa.2011.03.015
Abstract
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.
References in corpus (1)
Cited by in corpus (6)
- Small energy scattering for the Zakharov system with radial symmetry
- Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
- The nonlinear Brascamp-Lieb inequality for simple data
- Sharp spherically averaged Strichartz estimates for the Schrödinger equation
- Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions
- Local well-posedness of the Cauchy problem for the degenerate Zakharov system