Analyticity of rotational flows beneath solitary water waves

Real analyticity of streamlines is established of a gravity-driven steady flow of water in a two-dimensional channel enclosed by a supercritical solitary wave on the free surface and a rigid flat bed, for an arbitrary Hölder continuous vorticity, provided that the wave speed exceeds the horizontal fluid velocity throughout the flow. On the basis of the formulation of the solitary water-wave problem as a nonlinear elliptic boundary value problem in a fixed infinite strip, the proof uses the implicit function theorem for analytic operators. As key technical results, a priori estimates and spectral properties are derived for the linearized problem.