In this paper, we study the hydrostatic approximation for the 3D Oldroyd-B model. Firstly, we derive the hydrostatic approximate system for this model and prove the global well-posedness of the limit system with small analytic initial data in horizontal variable. Then we justify the hydrostatic limit strictly from the re-scaled Oldroyd-B model to the hydrostatic Oldroyd-B model and obtain the precise convergence rate.
@article{arxiv.2503.02638,
title = {On the hydrostatic approximation of 3D Oldroyd-B model},
author = {Marius Paicu and Tianyuan Yu and Ning Zhu},
journal= {arXiv preprint arXiv:2503.02638},
year = {2025}
}