TY - JOUR
T1 - Local well-posedness for the quantum Zakharov system in one spatial dimension
AU - Fang, Yung Fu
AU - Shih, Hsi Wei
AU - Wang, Kuan Hsiang
N1 - Funding Information:
The first two authors were partially supported by MOST(Taiwan) and by NCTS(Taiwan).
Publisher Copyright:
© 2017 World Scientific Publishing Company.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - 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.
AB - 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.
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U2 - 10.1142/S0219891617500059
DO - 10.1142/S0219891617500059
M3 - Article
AN - SCOPUS:85015980823
VL - 14
SP - 157
EP - 192
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
SN - 0219-8916
IS - 1
ER -