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

Yung Fu Fang, Hsi Wei Shih, Kuan Hsiang Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)157-192
Number of pages36
JournalJournal of Hyperbolic Differential Equations
Volume14
Issue number1
DOIs
Publication statusPublished - 2017 Mar 1

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Local Well-posedness
Quantum Systems
Sobolev Spaces
Electric Field
Deviation
Regularity
Zero

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

Cite this

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abstract = "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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Local well-posedness for the quantum Zakharov system in one spatial dimension. / Fang, Yung Fu; Shih, Hsi Wei; Wang, Kuan Hsiang.

In: Journal of Hyperbolic Differential Equations, Vol. 14, No. 1, 01.03.2017, p. 157-192.

Research output: Contribution to journalArticle

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