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Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-08-10 , DOI: 10.3934/dcds.2020313
Yi Guan , , Michal Fečkan , Jinrong Wang , , , ,

In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Different from the well-known homogeneous system in [14,20], we retain the turbulent fluxes and establish a new nonhomogeneous system of first order differential equations involving a term with the horizontal dependent. We present the existence and uniqueness of periodic solutions and show the Hyers-Ulam stability results for the nonhomogeneous systems under the mild conditions via the matrix theory. Further, we consider the nonhomogeneous systems with varying eddy viscosity coefficient and study systems with piecewise constants, systems with small oscillations, systems with rapidly varying coefficients and systems with slowly varying coefficients and give more continued results.

中文翻译:

大气埃克曼流的周期解和Hyers-Ulam稳定性

在本文中,我们研究了具有恒定涡流粘度的稳定大气埃克曼层中风的经典问题。与[1420],我们保留了湍流,并建立了一个新的一阶微分方程的非齐次系统,该系统涉及水平相关项。我们给出了周期解的存在性和唯一性,并通过矩阵理论证明了在温和条件下非齐次系统的Hyers-Ulam稳定性结果。此外,我们考虑了具有不同涡流系数的非均匀系统,并研究了具有分段常数的系统,具有小振荡的系统,具有快速变化的系数的系统和具有缓慢变化的系数的系统,并给出了更多的连续结果。
更新日期:2020-08-10
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