Counting Rayleigh-Benard instabilities for a variable viscosity
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Using spectral theory of compact operators, we provide a result for counting, given a frequency of oscillation and a Rayleigh number, the unstable modes for the Rayleigh-Benard system in the case of a variable viscosity. As exact solutions cannot be found (contrary to the classical literature), we provide a numerical method based a shooting method for solving the associated system of ODEs
