## Taiwanese Journal of Mathematics

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

#### Abstract

In this paper, we consider the quantum Zakharov system in one spatial dimension. We prove the global well-posedness of the system with $L^2$-Schrödinger data and some wave data. The regularity of the wave data is in the largest set. We give counterexamples for the boundary of the set. As the quantum parameter tends to zero, we formally recover the result of Colliander-Holmer-Tzirakis for the classical Zakharov system.

#### Article information

Source
Taiwanese J. Math., Volume 21, Number 2 (2017), 341-361.

Dates
First available in Project Euclid: 29 June 2017

https://projecteuclid.org/euclid.twjm/1498750956

Digital Object Identifier
doi:10.11650/tjm/7806

Mathematical Reviews number (MathSciNet)
MR3632519

Zentralblatt MATH identifier
06871321

#### Citation

Chen, Tsai-Jung; Fang, Yung-Fu; Wang, Kuan-Hsiang. Low Regularity Global Well-posedness for the Quantum Zakharov System in $1D$. Taiwanese J. Math. 21 (2017), no. 2, 341--361. doi:10.11650/tjm/7806. https://projecteuclid.org/euclid.twjm/1498750956

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