Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Kim, Jeongho
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G42150320
OpenAlex ID: W7223022171