Local Existence and Uniqueness of Navier–Stokes–Schrödinger System

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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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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Keywords

  • Initial value problem
  • Local solution
  • Navier–Stokes–Schrödinger system
  • Schrödinger maps

Mathematics Subject Classification

  • 35Q55
  • 35B65
  • 35B30
  • 35Q35