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arXiv · 1509.05355

Long Time Stability for Solutions of a Beta-Plane Equation

Tarek M. Elgindi·Klaus Widmayer
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Abstract

We prove stability for arbitrarily long times of the zero solution for the so-called $\beta$-plane equation, which describes the motion of a two-dimensional inviscid, ideal fluid under the influence of the Coriolis effect. The Coriolis force introduces a linear dispersive operator into the 2d incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, $L_1:=\frac{\partial_1}{|\nabla|^2}$, exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.

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Tarek M. Elgindi, Klaus Widmayer. 2015-09-17. Long Time Stability for Solutions of a Beta-Plane Equation. https://arxiv.org/abs/1509.05355

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