Global well-posedness and scattering for the quantum Zakharov system in 𝐿²

Fang, Yung-Fu; Nakanishi, Kenji

doi:10.1090/bproc/42

Global well-posedness and scattering for the quantum Zakharov system in $L^2$
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by Yung-Fu Fang and Kenji Nakanishi HTML | PDF

Proc. Amer. Math. Soc. Ser. B 6 (2019), 21-32

Abstract:

We study the Cauchy problem for the quantum Zakharov system in the class of square-integrable functions on the Euclidean space of general dimensions. The local well-posedness is proven for dimensions up to eight, together with global existence for dimensions up to five, as well as scattering for small initial data in dimensions greater than three.

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