论文标题
薄域中Navier-Stokes方程的静液压近似值的最佳Gevrey稳定性
Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain
论文作者
论文摘要
在本文中，我们研究了薄域中Navier-Stokes系统的静静力近似。当X变量中具有最佳索引3/2的Gevrey规则性的凸初始数据和y变量中的Sobolev规则性时，我们证明了从各向异性Navier-Stokes System到hydrystatic Navier-Stokes/prandtl System的限制。由于本文中的方法与ε无关，因此，通过相同的参数，我们还获得了静液压Navier-Stokes/prandtl系统在最佳的Gevrey空间中具有良好的作用。我们的结果改善了[14，34]中的Gevrey指数，其Gevrey指数为9/8。
In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in 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 is independent of ε, by the same argument, we also get the hydrostatic Navier-Stokes/Prandtl system is well-posedness in the optimal Gevrey space. Our results improve the Gevrey index in [14, 34] whose Gevrey index is 9/8 .
