Taiwanese Journal of Mathematics

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

Tsai-Jung Chen, Yung-Fu Fang, and Kuan-Hsiang Wang

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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

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

First available in Project Euclid: 29 June 2017

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Zentralblatt MATH identifier

Primary: 35L15: Initial value problems for second-order hyperbolic equations
Secondary: 35L70: Nonlinear second-order hyperbolic equations

quantum Zakharov system global well-posedness


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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