# 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} }

## 7 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…

### The three dimensional stochastic Zakharov system

- Mathematics
- 2023

We study the three dimensional stochastic Zakharov system in the energy space, where the Schrödinger equation is driven by linear multiplicative noise and the wave equation is driven by additive…

### 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 28 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…