Analyticity of rotational traveling gravity two-layer waves

The aim of this paper is to prove real analytic properties of all streamlines of two-dimensional steady rotational gravity water waves in two-layer flows. Provided that there are no stagnation points in the flow, we show that each streamline, including the free surface and the interface, is a real analytic curve if the height function is in Wloc2,infinity, which corresponds to an arbitrarily bounded and measurable vorticity function. Our results generalize those for the situation of single layer flow, and improve the results in the work by Chu, Escher, and Wang [Analyticity of rotational travelling waves in two-layer flows, submitted], where the analyticity is obtained for rotational two-layer water waves when the height function is in C2,alpha corresponding to a Holder continuous vorticity function.