OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN

IF 1.1 2区 数学 Q1 MATHEMATICS
Chao Wang, Yuxi Wang
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引用次数: 1

Abstract

In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When we have convex initial data with Gevrey regularity of optimal index $\frac {3}{2}$ in the x variable and Sobolev regularity in the y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper being independent of $\varepsilon $ , by the same argument, we also obtain the well-posedness of the hydrostatic Navier-Stokes/Prandtl system in the optimal Gevrey space. Our results improve upon the Gevrey index of $\frac {9}{8}$ found in [15, 35].
薄域NAVIER-STOKES方程流体静力近似的最优GEVREY稳定性
本文研究了薄域中Navier-Stokes系统的流体静力近似。当我们在x变量中具有最优指数$\frac{3}{2}$的Gevrey正则性和y变量中具有Sobolev正则性的凸初始数据时,我们证明了从各向异性Navier-Stokes系统到流体静力Navier-Stoke/Prandtl系统的极限。由于我们在本文中的方法与$\varepsilon$无关,通过同样的论点,我们还获得了最优Gevrey空间中流体静力Navier-Stokes/Prandtl系统的适定性。我们的结果改进了[15,35]中发现的$\frac{9}{8}$的Gevrey指数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.40
自引率
0.00%
发文量
54
审稿时长
>12 weeks
期刊介绍: The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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