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Roman Shvydkoy : Geometric optics method for the incompressible Euler equations

The method of geometric optics for incompressible Euler equations is used to study localized shortwave instabilities in ideal fluids. In linear approximation evolution of the shortwave ansatz can be described by a finite dimensional skew-product flow which determines all the linear instabilities coming from essential spectrum. In this talk we will discuss mathematical description of the method, aspects related to vanishing viscosity limit and application to the problem of inherent instability of ideal fluid flows.

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