Global regularity and large time behavior for some inviscid Oldroyd-B models in $\mathbb{R}^2$
Abstract
In this paper, we are concerned with global strong solutions and large time behavior for some inviscid Oldroyd-B models. We first establish the energy estimate and B-K-M criterion for the 2-D co-rotation inviscid Oldroyd-B model. Then, we obtain global strong solutions with large data in Sobolev space by proving the boundedness of vorticity. As a corollary, we prove global existence of the corresponding inviscid Hooke model near equilibrium. Furthermore, we present global existence for the 2-D co-rotation inviscid Oldroyd-B model in critical Besov space by a refined estimate in Besov spaces with index . Finally, we study large time behaviour for the noncorotation inviscid Oldroyd-B model. Applying the Fourier splitting method, we prove the decay rate for global strong solutions constructed by T. M. Elgindi and F. Rousset.
Cite
@article{arxiv.2107.12029,
title = {Global regularity and large time behavior for some inviscid Oldroyd-B models in $\mathbb{R}^2$},
author = {Wenjie Deng and Zhaonan Luo and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2107.12029},
year = {2023}
}