# 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} }

## 6 Citations

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

- Mathematics
- 2022

. 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…

### Global well-posedness and scattering for the Zakharov system at the critical space in three spatial dimensions with small and radial initial data

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### 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…

### An endline bilinear restriction estimate for paraboloids

- Mathematics
- 2022

. 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 ScienceJournal 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…

### MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (hybrid meeting)

- 2021

## References

SHOWING 1-10 OF 29 REFERENCES

### The Zakharov system in 4D radial energy space below the ground state

- MathematicsAmerican Journal of Mathematics
- 2021

We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in the energy space of four spatial dimensions that have less energy than…

### 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…

### Energy convergence for singular limits of Zakharov type systems

- Mathematics
- 2008

We prove existence and uniqueness of solutions to the Klein–Gordon–Zakharov system in the energy space H1×L2 on some time interval which is uniform with respect to two large parameters c and α. These…

### On the Zakharov and Zakharov-Schulman Systems

- Mathematics
- 1995

Abstract We consider the initial value problem for the Zakharov system [formula] which models the long wave Langmuir turbulence in a plasma. Using the standard iteration scheme in the original system…

### Well-posedness and scattering for the Zakharov system in four dimensions

- Mathematics
- 2015

The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are…

### Justification of the Zakharov Model from Klein–Gordon-Wave Systems

- Mathematics
- 2005

Abstract We study semilinear and quasilinear systems of the type Klein–Gordon-waves in the high-frequency limit. These systems are derived from the Euler–Maxwell system describing laser-plasma…

### Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case

- Mathematics
- 2006

We prove, for the energy critical, focusing NLS, that for data whose energy is smaller than that of the standing wave, and whose homogeneous Sobolev norm H^1 is smaller than that of the standing wave…

### On the Division Problem for the Wave Maps Equation

- MathematicsAnnals of PDE
- 2018

We consider Wave Maps into the sphere and give a new proof of small data global well-posedness and scattering in the critical Besov space, in any space dimension $$n \geqslant 2$$n⩾2. We use an…

### The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions

- Mathematics
- 2005

We obtain global well-posedness, scattering, and global $L^{\frac{2(n+2)}{n-2}}_{t,x}$ spacetime bounds for energy-space solutions to the energy-critical nonlinear Schrodinger equation in $\R_t\times…