# An Evans function for the linearised 2D Euler equations using Hill's determinant

@inproceedings{Dullin2021AnEF, title={An Evans function for the linearised 2D Euler equations using Hill's determinant}, author={Holger R. Dullin and Robert Marangell}, year={2021} }

We study the point spectrum of the linearisation of Euler’s equation for the ideal fluid on the torus about a shear flow. By separation of variables the problem is reduced to the spectral theory of a complex Hill’s equation. Using Hill’s determinant an Evans function of the original Euler equation is constructed. The Evans function allows us to completely characterise the point spectrum of the linearisation, and to count the isolated eigenvalues with non-zero real part. In particular this…

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