scholarly journals Global well-posedness and scattering for the quantum Zakharov system in $L^2$

2019 ◽  
Vol 6 (3) ◽  
pp. 21-32
Author(s):  
Yung-Fu Fang ◽  
Kenji Nakanishi
Keyword(s):  
Well Posedness ◽  
Zakharov System ◽  
Quantum Zakharov System

Local well-posedness for the quantum Zakharov system in one spatial dimension

2017 ◽  
Vol 14 (01) ◽  
pp. 157-192 ◽  
Author(s):  
Yung-Fu Fang ◽  
Hsi-Wei Shih ◽  
Kuan-Hsiang Wang
Keyword(s):  
Sobolev Space ◽  
Initial Data ◽  
Electric Field ◽  
Classical Result ◽  
Spatial Dimension ◽  
Well Posedness ◽  
Ion Density ◽  
Zakharov System ◽  
Quantum Parameter ◽  
Quantum Zakharov System

We consider the quantum Zakharov system in one spatial dimension and establish a local well-posedness theory when the initial data of the electric field and the deviation of the ion density lie in a Sobolev space with suitable regularity. As the quantum parameter approaches zero, we formally recover a classical result by Ginibre, Tsutsumi, and Velo. We also improve their result concerning the Zakharov system and a result by Jiang, Lin, and Shao concerning the quantum Zakharov system.

Local well-posedness for the quantum Zakharov system in three and higher dimensions

2021 ◽  
Vol 18 (02) ◽  
pp. 257-270
Author(s):  
Isao Kato
Keyword(s):  
Cauchy Problem ◽  
Type System ◽  
Higher Dimensions ◽  
Well Posedness ◽  
Zakharov System ◽  
Quantum Parameter ◽  
Fourier Restriction ◽  
The Cauchy Problem ◽  
The One ◽  
Quantum Zakharov System

We study the Cauchy problem associated with a quantum Zakharov-type system in three and higher spatial dimensions.Taking the quantum parameter to unit and developing Fourier restriction norm arguments, we establish local well-posedness property for wider range than the one known for the Zakharov system.

Local well-posedness for the quantum Zakharov system

2020 ◽  
Vol 18 (5) ◽  
pp. 1383-1411
Author(s):  
Yung-Fu Fang ◽  
Kuan-Hsiang Wang
Keyword(s):  
Well Posedness ◽  
Zakharov System ◽  
Quantum Zakharov System

scholarly journals Low Regularity Global Well-posedness for the Quantum Zakharov System in $1D$

2017 ◽  
Vol 21 (2) ◽  
pp. 341-361
Author(s):  
Tsai-Jung Chen ◽  
Yung-Fu Fang ◽  
Kuan-Hsiang Wang
Keyword(s):  
Well Posedness ◽  
Low Regularity ◽  
Zakharov System ◽  
Quantum Zakharov System
Sign in / Sign up

Export Citation Format

Share Document