We propose a continuous data assimilation (CDA) method to address the uniqueness problem for steady Navier-Stokes equations(NSE). The CDA method incorporates spatial observations into the NSE, and we prove that with sufficient observations, the CDA-NSE system is well-posed even for large data where multiple solutions may exist. This CDA idea is in general helpful to determine solution for non-uniqueness partial differential equations(PDEs).
@article{arxiv.2307.09538,
title = {Uniqueness of Steady Navier-Stokes under Large Data by Continuous Data Assimilation},
author = {Xuejian Li},
journal= {arXiv preprint arXiv:2307.09538},
year = {2023}
}