Numerical Analysis Seminars: Analysis of some nonlinear PDEs from multi-scale geophysical applications
15 November 2013 04:00 in CM 105
We investigate PDE systems from geophysical applications with multiple time scales, in which linear skew-self-adjoint operators of size 1/epsilon give rise to highly oscillatory solutions. Analysis is performed in justifying the limiting dynamics as epsilon goes to zero; furthermore, the analysis yields estimates on the difference between the multiscale solution and the limiting solution. We introduce a simple yet effective time-averaging technique which is especially useful in general domains where Fourier analysis is not applicable. With this technique, the nonlinear interaction of vortical and wave dynamics is O(epsilon) when averaged in time. Initial data are ill-prepared, i.e. not restricted to be near geostrophic balance.
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