Convolutions of singular measures and applications to the Zakharov system

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 (2)

• On the 2d Zakharov system with L^2 Schrödinger data
• A convolution estimate for two-dimensional hypersurfaces

Cited by in corpus (28)

• Stability of the Brascamp-Lieb constant and applications
• Small energy scattering for the Zakharov system with radial symmetry
• Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System
• Scattering for the Zakharov system in 3 dimensions
• On the nonlinear Brascamp-Lieb inequality
• Generalized Strichartz estimates and scattering for 3D Zakharov system
• Behaviour of the Brascamp--Lieb constant
• Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
• The fourth order nonlinear Schrodinger limit for quantum Zakharov system
• Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D
• Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrödinger equations
• Local well-posedness for the Zakharov system on multidimensional torus
• Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation
• Well-posedness and scattering for the Zakharov system in four dimensions
• Trigonometric time integrators for the Zakharov system
• Local Well-Posedness for the Zakharov System in Dimension $d⩽3$
• The Zakharov system in dimension $d⩾4$
• On one dimensional Quantum Zakharov system
• Lower bound for the rate of blow-up of singular solutions of the Zakharov system in ${\mathbb{R}}^3$
• Scattering and well-posedness for the Zakharov system at a critical space in four and more spatial dimensions
• Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
• The nonlinear Brascamp-Lieb inequality for simple data
• Local well-posedness for the Zakharov system in dimension $d=2,3$
• Smoothing for the Zakharov & Klein-Gordon-Schrödinger Systems on Euclidean Spaces
• Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D
• Local well-posedness of the Cauchy problem for the degenerate Zakharov system
• Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions
• Sharp spherically averaged Strichartz estimates for the Schrödinger equation