# Global wellposedness for the energy-critical Zakharov system below the ground state

@article{Candy2020GlobalWF,
title={Global wellposedness for the energy-critical Zakharov system below the ground state},
author={Timothy Candy and Sebastian Herr and Kenji Nakanishi},
journal={arXiv: Analysis of PDEs},
year={2020}
}
• Published 20 May 2020
• Mathematics
• arXiv: Analysis of PDEs
6 Citations

### Minimal non-scattering solutions for the Zakharov system

. We consider the Zakharov system in the energy critical dimension d = 4 with energy below the ground state. It is known that below the ground state solutions exist globally in time, and scatter in

### Norm inflation for the Zakharov system

. 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

### An endline bilinear restriction estimate for paraboloids

. We prove an L 2 × L 2 → L qt L rx bilinear adjoint Fourier restriction estimate for n -dimensional elliptic paraboloids, with n ≥ 2 and 1 ≤ q ≤ ∞ , 1 ≤ r ≤ 2 being on the endline 1 q = n +12

### The Zakharov system in dimension $d \geq 4$

• Computer Science
Journal of the European Mathematical Society
• 2022
. The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classi-cal Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of

• 2021

## References

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• Mathematics
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