PreprintCC BY 4.0arXiv
Local well-posedness of the two-dimensional Incompressible Schrödinger flow
Abstract
We consider the incompressible Schrödinger flow (ISF), an efficient model for simulating incompressible inviscid fluids introduced by Chern et al. \cite{C17,CKPSW16}, on a bounded, simply connected two-dimensional domain. After transforming it into the director formulation, the equation becomes the Schrödinger map (or the Landau--Lifshitz equation) transported by a velocity field generated from the director itself via Biot--Savart law. We show that the director formulation has a unique local-in-time strong solution. Then, we lift the solution to the director formulation to the spinor, and conclude that it is indeed a unique solution to the ISF. This result is a first rigorous analysis on ISF, a widely used computational model.
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BibTeX
@misc{kim2026local,
title = {{Local well-posedness of the two-dimensional Incompressible Schrödinger flow}},
author = {Jeongho Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24933},
eprint = {2610.24933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24933},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local well-posedness of the two-dimensional Incompressible Schrödinger flow
AU - Jeongho Kim
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24933
UR - https://arxiv.org/abs/2610.24933
AB - We consider the incompressible Schrödinger flow (ISF), an efficient model for simulating incompressible inviscid fluids introduced by Chern et al. \cite{C17,CKPSW16}, on a bounded, simply connected two-dimensional domain. After transforming it into the director formulation, the equation becomes the Schrödinger map (or the Landau--Lifshitz equation) transported by a velocity field generated from the director itself via Biot--Savart law. We show that the director formulation has a unique local-in-time strong solution. Then, we lift the solution to the director formulation to the spinor, and conclude that it is indeed a unique solution to the ISF. This result is a first rigorous analysis on ISF, a widely used computational model.
ER -