On one dimensional quantum Zakharov system

Jin Cheng Jiang*, Chi Kun Lin, Shuanglin Shao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


In this paper, we discuss the properties of one dimensional quantum Zakharov system which describes the nonlinear interaction between the quantum Langmuir and quantum ion-acoustic waves. The system (1a)-(1b) with initial data (E(0), n(0), ∂tn(0)) ϵ Hk ⊕ Hl ⊕ Hl-2 is local well-posedness in low regularity spaces (see Theorem 1.1 and Figure 1). Especially, the low regularity result for k satisfies -3/4 < k ≤ -1/4 is obtained by using the key observation that the convoluted phase function is convex and careful bilinear analysis. The result can not be obtained by using only Strichartz inequalities for "Schrödinger" waves.

Original languageEnglish
Pages (from-to)5445-5475
Number of pages31
JournalDiscrete and Continuous Dynamical Systems
Issue number10
Publication statusPublished - Oct 2016


  • Cauchy problem
  • Local well-posedness
  • Low regularity
  • One dimensional
  • Quantum Zakharov system

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