Global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models
Abstract
This paper is devoted to global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models with center diffusion. By virtue of the properties of Calderon-Zygmund operator and the Littlewood-Paley decomposition theory, we firstly prove that the 2-D co-rotation inviscid Oldroyd-B model admits global weak solutions with some large data under different integrability conditions. Furthermore, we prove the energy conservation of weak solutions for the co-rotation case. These obtained results generalize and cover the classical results for the Euler equation. Moreover, we establish global weak solutions with small data for the 2-D noncorotation inviscid Oldroyd-B model without damping. Finally, we prove optimal decay rate of global weak solutions for the noncorotation case by the improved Fourier splitting method.
Keywords
Cite
@article{arxiv.2307.10566,
title = {Global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models},
author = {Wenjie Deng and Zhaonan Luo and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2307.10566},
year = {2023}
}
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44 pages