Kato, Isao Local well-posedness for the quantum Zakharov system in three and higher dimensions. (English) Zbl 1480.35103 J. Hyperbolic Differ. Equ. 18, No. 2, 257-270 (2021). Summary: We study the Cauchy problem associated with a quantum Zakharov-type system in three and higher spatial dimensions. Taking the quantum parameter to unit and developing Fourier restriction norm arguments, we establish local well-posedness property for wider range than the one known for the Zakharov system. Cited in 2 Documents MSC: 35G55 Initial value problems for systems of nonlinear higher-order PDEs 35Q40 PDEs in connection with quantum mechanics Keywords:low regularity; Bourgain space; high frequency quantum Langmuir waves; low frequency quantum ion acoustic waves × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bejenaru, I. and Herr, S., Convolutions of singular measures and applications to the Zakharov system, J. Funct. 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