Global regularity and large time behavior for some inviscid Oldroyd-B models in $\mathbb{R}^2$

Wenjie Deng; Zhaonan Luo; Zhaoyang Yin

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arXiv · 2107.12029

Global regularity and large time behavior for some inviscid Oldroyd-B models in $\mathbb{R}^2$

Wenjie Deng·Zhaonan Luo·Zhaoyang Yin

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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 $0$. Finally, we study large time behaviour for the noncorotation inviscid Oldroyd-B model. Applying the Fourier splitting method, we prove the $H^1$ decay rate for global strong solutions constructed by T. M. Elgindi and F. Rousset.

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Wenjie Deng, Zhaonan Luo, Zhaoyang Yin. 2021-07-26. Global regularity and large time behavior for some inviscid Oldroyd-B models in $\mathbb{R}^2$. https://arxiv.org/abs/2107.12029

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