Low regularity global well-posedness for the quantum Zakharov system in 1D

Tsai Jung Chen; Yung Fu Fang; Kuan Hsiang Wang

doi:10.11650/tjm/7806

Low regularity global well-posedness for the quantum Zakharov system in 1D

Tsai Jung Chen, Yung Fu Fang, Kuan Hsiang Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In this paper, we consider the quantum Zakharov system in one spatial dimension. We prove the global well-posedness of the system with L²-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.

Original language	English
Pages (from-to)	341-361
Number of pages	21
Journal	Taiwanese Journal of Mathematics
Volume	21
Issue number	2
DOIs	https://doi.org/10.11650/tjm/7806
Publication status	Published - 2017

All Science Journal Classification (ASJC) codes

General Mathematics

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10.11650/tjm/7806

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abstract = "In this paper, we consider the quantum Zakharov system in one spatial dimension. We prove the global well-posedness of the system with L2-Schr{\"o}dinger 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.",

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AU - Fang, Yung Fu

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AB - In this paper, we consider the quantum Zakharov system in one spatial dimension. We prove the global well-posedness of the system with L2-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.

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Low regularity global well-posedness for the quantum Zakharov system in 1D

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