### Effect of magnetic field on thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid.

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We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to $\epsilon $. This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.