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• W4386482007 abstract "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]." @default.
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• W4386482007 date "2023-09-06" @default.
• W4386482007 modified "2023-09-27" @default.
• W4386482007 title "OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN" @default.
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• W4386482007 doi "https://doi.org/10.1017/s1474748023000282" @default.
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