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).

Keywords

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

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Funding

National Natural Science Foundation of China(11771415)