Convolutions of singular measures and applications to the Zakharov system

By I. Bejenaru, Sebastian Herr. 2010

90 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/162e4671175bfed1f01d3dc98396b86c3a682176

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D (2019, methodology): “This estimate is called the nonlinear Loomis-Whitney inequality and was applied to the Cauchy problem of the Zakharov system on R(2) and R(3) by Bejenaru, Herr, Holmer, and Tataru in [1] and by Bejenaru and Herr in [2], respectively.”
Small Energy Scattering for the Zakharov System with Radial Symmetry (2012, background): “The improvement was obtained to the critical regularity in [5, 2] for d = 1, 2, and to the full subcritical regularity in [5, 1] for d ≥ 4, d = 3.”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, methodology): “This has provided a mechanism through which unexpected techniques may be brought to bear on difficult curvature-related problems in harmonic analysis and PDE; see [20], [21], [23],[4] and [36].”