运输噪声下的埃克曼边界层
Ekman Boundary Layers Under Transport Noise
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中文总结 AI 辅助
本文研究三维旋转纳维-斯托克斯方程在运输噪声下，垂直粘性消失与快速旋转联合极限，构造鞅弱解并证明其收敛到带阻尼的二维随机方程分层强解，阻尼系数由粘性与旋转速率比决定。
中文摘要 AI 辅助
我们考虑一个在水平平板之间、具有运输-拉伸噪声的三维旋转纳维-斯托克斯方程，并研究垂直粘性消失与快速旋转的联合极限。我们的驱动噪声仅依赖于水平坐标，其垂直分量随粘性一起消失。假设初始数据是纯水平的，我们构造了鞅弱解，这些解在 $L^2_{\omega}L^\infty_tL^2_x$ 中收敛到带阻尼的二维随机纳维-斯托克斯方程的分层强解。阻尼系数依赖于垂直粘性与逆旋转速率之比的极限。
英文摘要
We consider a 3D rotating Navier-Stokes equation with transport-stretching noise, posed between two horizontal plates, and study the joint limit of vanishing vertical viscosity and rapid rotation. Our driving noise depends only on the horizontal coordinates and its vertical component vanishes with the viscosity. Provided that the initial data is purely horizontal, we construct martingale weak solutions which converge in $L^2_ωL^\infty_tL^2_x$ to the layered strong solution of a 2D stochastic Navier-Stokes equation with damping. The damping coefficient is dependent on the limit of the ratio between vertical viscosity and inverse rotation rate.
发表机构
- EPFL（洛桑联邦理工学院）
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