论文标题
在二维中，cauchy的问题是无粘性和非延伸的Oldroyd-B模型
The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions
论文作者
论文摘要
[T. M. Elgindi，F。Rousset，Commun。纯应用。数学。 68（2015），2005--2021]，其中为任意大型初始数据建立了强大解决方案的全球存在和独特性。如[A. V. Bhave，R。C。Armstrong，R。A。Brown，J。Chem。物理。 95（1991），2988--3000]，扩散系数明显小于其他效果，研究非排除模型很有趣。在目前的工作中，我们通过得出一些统一的规律性估计并采取消失的扩散限制，从而获得了非扩展模型的强大解决方案的全球存在和独特性。此外，研究了解决方案的较大时间行为，并获得了每个空间衍生物的最佳时间段率。主要挑战的重点是缺乏系统的耗散和规律性影响，以及二维环境中较慢的衰变。采用了光谱分析和傅立叶分裂方法的组合。
A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by [T. M. Elgindi, F. Rousset, Commun. Pure Appl. Math. 68 (2015), 2005--2021] where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by [A. V. Bhave, R. C. Armstrong, R. A. Brown, J. Chem. Phys. 95(1991), 2988--3000], the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present work, we obtain the global-in-time existence and uniqueness of the strong solution to the non-diffusive model with small initial data via deriving some uniform regularity estimates and taking vanishing diffusion limits. In addition, the large time behavior of the solution is studied and the optimal time-decay rates for each order of spatial derivatives are obtained. The main challenges focus on the lack of dissipation and regularity effects of the system and on the slower decay in the two-dimensional settings. A combination of the spectral analysis and the Fourier splitting method is adopted.
