Study of core annular flow of two liquids of different viscosity generates two new amplitude equations of the Kuramoto-Sivashinsky (KS) type. In the first an integral operator of dispersive nature appends the KS. It modifies the bifurcation structure of the KS and delays parametrically the appearances of a specific pattern. The second modification, specific to cylindrical geometry, is due to a sensitive part in the curvature dispensed within a conventional expansion. When retained, it may cause a linearly unstable interface to rupture and to form, experimentally observed, bubbles.