Linear Inviscid Damping for the $$eta $$-Plane Equation
Linear Inviscid Damping for the $$eta $$-Plane Equation
复制标题
$$eta $$-平面方程的线性无粘阻尼
DOI：
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发表时间：
2018
影响因子：
2.4
通讯作者：
Hao Zhu
中科院分区：
文献类型：
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作者：
Dongyi Wei;Zhifei Zhang;Hao Zhu
本文研究了切变流作用下线性化的平面方程的线性无粘阻尼解。我们发展了一种新的方法来给出一类单调剪切流速度的显式衰减率。该方法基于波动方程SPRIT中的时空估计和矢量场方法。对于包括正弦流在内的一般剪切流，我们还建立了基于Wei-Zhang-赵在引用{WZZ2}中介绍的紧致性方法的极限吸收原理，从而证明了线性阻尼。主要的困难是由于科里奥利效应，Rayleigh-Kuo方程有更多的奇点，使得紧致性的论证变得更加复杂和微妙。
In this paper, we study the linear inviscid damping for the linearized $eta$-plane equation around shear flows. We develop a new method to give the explicit decay rate of the velocity for a class of monotone shear flows. This method is based on the space-time estimate and the vector field method in sprit of the wave equation. For general shear flows including the Sinus flow, we also prove the linear damping by establishing the limiting absorption principle, which is based on the compactness method introduced by Wei-Zhang-Zhao in cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more singular points due to the Coriolis effects so that the compactness argument becomes more involved and delicate.
线性化二维欧拉方程中的涡轴对称化、无粘阻尼和涡耗
影响因子：
2.8
作者：
Bedrossian, Jacob;Coti Zelati, Michele;Vicol, Vlad
通讯作者：
Vicol, Vlad
影响因子：
1.7
作者：
E. Grenier;Toan T. Nguyen;F. Rousset;A. Soffer
通讯作者：
E. Grenier;Toan T. Nguyen;F. Rousset;A. Soffer