We prove stability for arbitrarily long times of the zero solution for the so-called β-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 two-dimensional incompressible Euler equations, thus making this problem amenable to an analysis from the point of view of nonlinear dispersive equations. The dispersive operator, L1:(Formula presented.), exhibits good decay, but has numerous unfavorable properties, chief among which are its anisotropy and its behavior at small frequencies.
|Original language||English (US)|
|Number of pages||47|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Aug 2017|
All Science Journal Classification (ASJC) codes
- Applied Mathematics