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Local Existence and Uniqueness of Navier–Stokes–Schrödinger System

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Abstract

In this article, we prove that there exists a unique local smooth solution for the Cauchy problem of the Navier–Stokes–Schrödinger system. Our methods rely upon approximating the system with a sequence of perturbed system and parallel transport and are closer to the one in Ding and Wang (Sci China 44(11):1446–1464, 2001) and McGahagan (Commun Partial Differ Equ 32(1–3):375–400, 2007).

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11771415).

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Authors and Affiliations

  1. CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Jiaxi Huang

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Jiaxi Huang

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  1. Jiaxi Huang
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Correspondence to Jiaxi Huang.

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Huang, J. Local Existence and Uniqueness of Navier–Stokes–Schrödinger System. Commun. Math. Stat. 9, 101–118 (2021). https://doi.org/10.1007/s40304-020-00214-7

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  • DOI: https://doi.org/10.1007/s40304-020-00214-7

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