# Convolutions of singular measures and applications to the Zakharov system

@article{Bejenaru2011ConvolutionsOS, title={Convolutions of singular measures and applications to the Zakharov system}, author={Ioan Bejenaru and Sebastian Herr}, journal={Journal of Functional Analysis}, year={2011}, volume={261}, pages={478-506} }

## 72 Citations

Norm inflation for the Zakharov system

- Mathematics
- 2022

. We prove norm inﬂation in new regions of Sobolev regularities for the scalar Zakharov system in the spatial domain R d for arbitrary d ∈ N . To this end, we apply abstract considerations of…

Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2015

We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The…

Local well-posedness for the Zakharov system on the multidimensional torus

- Mathematics
- 2011

The initial value problem of the Zakharov system on the two dimensional torus with general period is shown to be locally well posed in the Sobolev spaces of optimal regularity, including the energy…

WELL-POSEDNESS FOR THE CAUCHY PROBLEM OF THE KLEIN-GORDON-ZAKHAROV SYSTEM IN 2 D

- Mathematics
- 2017

This paper is concerned with the Cauchy problem of the KleinGordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time…

Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

- Mathematics
- 2016

This paper is concerned with the Cauchy problem of the Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time…

Local well-posedness for the Klein-Gordon-Zakharov system in 3D

- MathematicsDiscrete & Continuous Dynamical Systems - A
- 2021

We study the Cauchy problem for the Klein-Gordon-Zakharov system in 3D with low regularity data. We lower down the regularity to the critical value with respect to scaling up to the endpoint. The…

Global Well-posedness of the Adiabatic Limit of Quantum Zakharov System in 1 D

- Mathematics
- 2019

In this paper, we prove the low-regularity global well-posedness of the adibatic limit of the Quantum Zakharov system and consider its semi-classical limit, i.e., the convergence of the model…

The Zakharov system in dimension $d \geqslant 4$

- Mathematics
- 2019

The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of initial…

Global Well-posedness of the Adiabatic Limit of Quantum Zakharov System in 1D

- Mathematics
- 2019

In this paper, we prove the low-regularity global well-posedness of the adibatic limit of the Quantum Zakharov system and consider its semi-classical limit, i.e., the convergence of the model…

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