| Abstract: |
| We illustrate the state of art of a simple, but robust, procedure to study the asymptotic behavior of perturbations of a vorticity solving the Euler equations in Yudovich`s class. The perturbation can be with/without a vanishing source term and/or a vanishing viscosity parameter (Navier--Stokes equations, for instance), and the setup of the problem can be within the entire two-dimensional space or torus.
Broadly speaking, we show how the rate of convergence of the approximate vorticity can be improved by understanding the evanescence of some appropriately post-determined high frequencies. We also comment on another application of our method in the asymptotic analysis of a Plasma model within the non-relativistic regime. |
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