English

Global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models

Analysis of PDEs 2023-07-21 v1

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